Ruthven, Kenneth; Deaney, Rosemary; Hennessy, Sara
2009-01-01
From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater…
An Execution Algorithm for UML Activity Graphs
Eshuis, H.; Wieringa, Roelf J.; Gogolla, Martin; Kobryn, Cris
2001-01-01
We present a real-time execution semantics for UML activity graphs that is intended for workflow modelling. The semantics is defined in terms of execution algorithms that define how components of a workflow system execute an activity graph. The semantics stays close to the semantics of UML state
2016-01-01
Background Mindfulness training (MT) programs represent an approach to attention training with well-validated mental health benefits. However, research supporting MT efficacy is based predominantly on weekly-meeting, facilitator-led, group-intervention formats. It is unknown whether participants might benefit from neurofeedback-assisted, technology-supported MT (N-tsMT), in which meditation is delivered individually, without the need for a facilitator, travel to a training site, or the presen...
A NOVEL GRAPH MODEL FOR E-MAIL FORENSICS: EVIDENCE ACTIVITY ANALYSIS GRAPH
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Sridhar Neralla
2013-10-01
Full Text Available This work puts forward a novel technique for evidence analysis that assist cyber forensics expert for analyzing cyber crime episode in an effective manner. Novelty in Evidence Activity Analysis Graph is reflection of activities involved in the cyber crime that are represented as nodes along with stylometric analysis. In this pieceof work email based cyber crime incident is considered for study and that incident is represented in Evidence Activity Analysis Graph to fix the suspect. Comparisons between various graphs that are used in cyber forensics were also discussed in this paper. This model establishes relationships between various activities that were happened in the cyber crime.
Exploration of Tensions in a Mobile-Technology Supported Fieldtrip: An Activity Theory Perspective
Lai, Chih-Hung; Chen, Fei-Ching; Yang, Jie-Chi
2014-01-01
The purpose of this study was to analyze how mobile technologies were incorporated and implemented in an outdoor learning activity. Two classes of primary school students participated in the experiment. Using activity theory as an analytical framework, it is found that underlying tensions provided rich insights into system dynamics and that…
Activities involving aeronautical, space science, and technology support for minority institutions
1993-01-01
The Final Report addressed the activities with which the Interracial Council for Business Opportunity (ICBO) was involved over the past 12 months. ICBO was involved in the design and development of a CARES Student Tracking System Software (CARES). Cares is intended to provide an effective means of maintaining relevant current and historical information on NASA-funded students through a range of educational program initiatives. ICBP was extensively involved in the formation of a minority university consortium amd implementation of collaborative research activities by the consortium as part of NASA's Mission to Planet Earth/Earth Observing System. ICBO was involved in the formation of an HBCU/MI Consortium to facilitate technology transfer efforts to the small and minority business community in their respective regions.
Inflammatory aetiology of human myometrial activation tested using directed graphs.
Directory of Open Access Journals (Sweden)
2005-07-01
Full Text Available THERE ARE THREE MAIN HYPOTHESES FOR THE ACTIVATION OF THE HUMAN UTERUS AT LABOUR: functional progesterone withdrawal, inflammatory stimulation, and oxytocin receptor activation. To test these alternatives we have taken information and data from the literature to develop causal pathway models for the activation of human myometrium. The data provided quantitative RT-PCR results on key genes from samples taken before and during labour. Principal component analysis showed that pre-labour samples form a homogenous group compared to those during labour. We therefore modelled the alternative causal pathways in non-labouring samples using directed graphs and statistically compared the likelihood of the different models using structural equations and D-separation approaches. Using the computer program LISREL, inflammatory activation as a primary event was highly consistent with the data (p = 0.925, progesterone withdrawal, as a primary event, is plausible (p = 0.499, yet comparatively unlikely, oxytocin receptor mediated initiation is less compatible with the data (p = 0.091. DGraph, a software program that creates directed graphs, produced similar results (p= 0.684, p= 0.280, and p = 0.04, respectively. This outcome supports an inflammatory aetiology for human labour. Our results demonstrate the value of directed graphs in determining the likelihood of causal relationships in biology in situations where experiments are not possible.
Sampling frequency affects ActiGraph activity counts
DEFF Research Database (Denmark)
Brønd, Jan Christian; Arvidsson, Daniel
in Matlab and sampled at frequencies of 30-100 Hz. Also, acceleration signals during indoor walking and running were sampled at 30 Hz using the ActiGraph GT3X and resampled in Matlab to frequencies of 40-100 Hz. All data was processed with the ActiLife software.Results: Acceleration frequencies between 5....... The difference increased with increasing activity intensity, with up to 1000 counts per minute at fast running.Discussion & conclusions: Activity counts from vigorous physical activity is highly attenuated with the ActiLife software. High frequency movement and noise information escape the bandpass filter...
Fast Graph Partitioning Active Contours for Image Segmentation Using Histograms
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Nath SumitK
2009-01-01
Full Text Available Abstract We present a method to improve the accuracy and speed, as well as significantly reduce the memory requirements, for the recently proposed Graph Partitioning Active Contours (GPACs algorithm for image segmentation in the work of Sumengen and Manjunath (2006. Instead of computing an approximate but still expensive dissimilarity matrix of quadratic size, , for a 2D image of size and regular image tiles of size , we use fixed length histograms and an intensity-based symmetric-centrosymmetric extensor matrix to jointly compute terms associated with the complete dissimilarity matrix. This computationally efficient reformulation of GPAC using a very small memory footprint offers two distinct advantages over the original implementation. It speeds up convergence of the evolving active contour and seamlessly extends performance of GPAC to multidimensional images.
Undergraduate Student Construction and Interpretation of Graphs in Physics Lab Activities
Nixon, Ryan S.; Godfrey, T. J.; Mayhew, Nicholas T.; Wiegert, Craig C.
2016-01-01
Lab activities are an important element of an undergraduate physics course. In these lab activities, students construct and interpret graphs in order to connect the procedures of the lab with an understanding of the related physics concepts. This study investigated undergraduate students' construction and interpretation of graphs with best-fit…
Undergraduate Student Construction and Interpretation of Graphs in Physics Lab Activities
Nixon, Ryan S.; Godfrey, T. J.; Mayhew, Nicholas T.; Wiegert, Craig C.
2016-01-01
Lab activities are an important element of an undergraduate physics course. In these lab activities, students construct and interpret graphs in order to connect the procedures of the lab with an understanding of the related physics concepts. This study investigated undergraduate students' construction and interpretation of graphs with best-fit…
Technology support for participatory budgeting
DEFF Research Database (Denmark)
Rose, Jeremy; Rios, Jesus; Lippa, Barbara
2010-01-01
Participatory budgeting is a reasonably well-established governance practice, particularly in South America. It is information and communication rich - making it well suited for modern technology support; in addition, the widespread participation of many citizens is difficult to achieve without...
Conway, Lorraine
This packet of student materials contains a variety of worksheet activities dealing with science graphs and science word games. These reproducible materials deal with: (1) bar graphs; (2) line graphs; (3) circle graphs; (4) pictographs; (5) histograms; (6) artgraphs; (7) designing your own graphs; (8) medical prefixes; (9) color prefixes; (10)…
SIMULATION OF DRIVER’S LOCOMOTIVE-HANDLING ACTIVITY USING THE THEORY OF FUZZY GRAPHS
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T. V. Butko
2015-03-01
Full Text Available Purpose. The efficiency and safety of locomotive control improving is important and relevant scientific and practical problem. Every driver during the trains-handling bases on his experience and knowledge, that is why the compilation and detection the most efficient ways to control the locomotive-handling is one of the stages of measures development to reduce transportation costs. The purpose of this paper is a formalization process description of locomotive-handling and quality parameters determination of this process. Methodology. In order to achieve this goal the theory of fuzzy probabilistic graphs was used. Vertices of the graph correspond to the events start and end operations at train-handling. The graph arcs describe operations on train-handling. Graph consists of thirteen peaks corresponding to the main control actions of the engine-driver. The weighting factors of transitions between vertices are assigned by fuzzy numbers. Their values were obtained by expert estimates. Fuzzy probabilities and transition time are presented as numbers with trapezoidal membership function. Findings. Using successive merging of parallel arcs, loops and vertices elimination, the equivalent fuzzy graph of train-handling and the corresponding L-matrix were obtained. Equivalent graph takes into account separately activity of the driver during normal operation and during emergency situations. Originality. The theoretical foundations of describing process formalization in driver’s locomotive-handling activity were developed using the fuzzy probabilistic graph. The parameters characterizing the decision-making process of engineer were obtained. Practical value. With the resulting model it is possible to estimate the available reserves for the quality improvement of locomotive-handling. Reduction in the time for decision-making will lead to the approximation the current mode of control to the rational one and decrease costs of hauling operations. And reduction
Botzer, Galit; Yerushalmy, Michal
2008-01-01
This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of…
Directory of Open Access Journals (Sweden)
Smith Malaina
2010-09-01
Full Text Available Abstract Background Suboptimal diet and physical inactivity are prevalent, co-occurring chronic disease risk factors, yet little is known about how to maximize multiple risk behavior change. Make Better Choices, a randomized controlled trial, tests competing hypotheses about the optimal way to promote healthy change in four bundled risk behaviors: high saturated fat intake, low fruit and vegetable intake, low physical activity, and high sedentary leisure screen time. The study aim is to determine which combination of two behavior change goals - one dietary, one activity - yields greatest overall healthy lifestyle change. Methods/Design Adults (n = 200 with poor quality diet and sedentary lifestyle will be recruited and screened for study eligibility. Participants will be trained to record their diet and activities onto a personal data assistant, and use it to complete two weeks of baseline. Those who continue to show all four risk behaviors after baseline recording will be randomized to one of four behavior change prescriptions: 1 increase fruits and vegetables and increase physical activity, 2 decrease saturated fat and increase physical activity, 3 increase fruits and vegetable and decrease saturated fat, or 4 decrease saturated fat and decrease sedentary activity. They will use decision support feedback on the personal digital assistant and receive counseling from a coach to alter their diet and activity during a 3-week prescription period when payment is contingent upon meeting behavior change goals. They will continue recording on an intermittent schedule during a 4.5-month maintenance period when payment is not contingent upon goal attainment. The primary outcome is overall healthy lifestyle change, aggregated across all four risk behaviors. Discussion The Make Better Choices trial tests a disseminable lifestyle intervention supported by handheld technology. Findings will fill a gap in knowledge about optimal goal prescription to
Mining bipartite graphs to improve semantic pedophile activity detection
Fournier, Raphaël; Danisch, Maximilien
2014-01-01
International audience; Peer-to-peer (P2P) networks are popular to exchange large volumes of data through the Internet. Paedophile activity is a very important topic for our society and some works have recently attempted to gauge the extent of paedophile exchanges on P2P networks. A key issue is to obtain an efficient detection tool, which may decide if a sequence of keywords is related to the topic or not. We propose to use social network analysis in a large dataset from a P2P network to imp...
SYNTHESIS METHODOLOGY FOR ACTIVE ELEMENT USING IMPEDANCES –BASED BOND GRAPH METHODS
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Nasta TANASESCU
2004-12-01
Full Text Available This paper introduces a synthesis methodology for active elements within systems that uses frequency response function as a basis for describing required behavior. The method is applicable in the design of a new system or in the retrofit of an existing system in which an active element is required or desired. The two basis principles of bond graph modeling are the “reticulation principle” which decomposes a physical into elemental physical laws represented as network elements interacting through ports and the “power postulate” which assembles the complete model through a network of power flows representing the exchange of energy between the elements. Moreover the bond graph model leads to a rigorous definitions of the structure of the associated dynamical equations.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Directory of Open Access Journals (Sweden)
Hoi-Chi Woo
Full Text Available Certain hand activities cause deformation and displacement of the median nerve at the carpal tunnel due to the gliding motion of tendons surrounding it. As smartphone usage escalates, this raises the public's concern whether hand activities while using smartphones can lead to median nerve problems.The aims of this study were to 1 develop kinematic graphs and 2 investigate the associated deformation and rotational information of median nerve in the carpal tunnel during hand activities.Dominant wrists of 30 young adults were examined with ultrasonography by placing a transducer transversely on their wrist crease. Ultrasound video clips were recorded when the subject performing 1 thumb opposition with the wrist in neutral position, 2 thumb opposition with the wrist in ulnar deviation and 3 pinch grip with the wrist in neutral position. Six still images that were separated by 0.2-second intervals were then captured from the ultrasound video for the determination of 1 cross-sectional area (CSA, 2 flattening ratio (FR, 3 rotational displacement (RD and 4 translational displacement (TD of median nerve in the carpal tunnel, and these collected information of deformation, rotational and displacement of median nerve were compared between 1 two successive time points during a single hand activity and 2 different hand motions at the same time point. Finally, kinematic graphs were constructed to demonstrate the mobility of median nerve during different hand activities.Performing different hand activities during this study led to a gradual reduction in CSA of the median nerve, with thumb opposition together with the wrist in ulnar deviation causing the greatest extent of deformation of the median nerve. Thumb opposition with the wrist in ulnar deviation also led to the largest extent of TD when compared to the other two hand activities of this study. Kinematic graphs showed that the motion pathways of median nerve during different hand activities were complex
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Fretter, Christoph; Lesne, Annick; Hilgetag, Claus C.; Hütt, Marc-Thorsten
2017-02-01
Simple models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering. Here we analyze how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology. Our findings are interpreted in the context of network reverberations and self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience.
Institute of Scientific and Technical Information of China (English)
傅育熙
1998-01-01
The paper proposes reaction graphs as graphical representations of computational objects.A reaction graph is a directed graph with all its arrows and some of its nodes labeled.Computations are modled by graph rewriting of a simple nature.The basic rewriting rules embody the essence of both the communications among processes and cut-eliminations in proofs.Calculi of graphs are ideentified to give a formal and algebraic account of reaction graphs in the spirit of process algebra.With the help of the calculi,it is demonstrated that reaction graphs capture many interesting aspects of computations.
Comparison of Sedentary Estimates between activPAL and Hip- and Wrist-Worn ActiGraph
DEFF Research Database (Denmark)
Koster, Annemarie; Shiroma, Eric J; Caserotti, Paolo
2016-01-01
Purpose Sedentary behavior is an emerging independent health risk factor. The accuracy of measuring sedentary time using accelerometers may depend on the wear location. This study in older adults evaluated the accuracy of various hip- and wrist-worn ActiGraph accelerometer cutoff points to define...... sedentary time using the activPAL as the reference method. Methods Data from 62 adults (mean age, 78.4 yr) of the Aging Research Evaluating Accelerometry study were used. Participants simultaneously wore an activPAL accelerometer on the thigh and ActiGraph accelerometers on the hip, dominant......, and nondominant wrist for 7 d in a free-living environment. Using the activPAL as the reference criteria, we compared classification of sedentary time to hip-worn and wrist-worn ActiGraph accelerometers over a range of cutoff points for both 60-s and 15-s epochs. Results The optimal cutoff point for the hip...
What graph theory actually tells us about resting state interictal MEG epileptic activity.
Niso, Guiomar; Carrasco, Sira; Gudín, María; Maestú, Fernando; Del-Pozo, Francisco; Pereda, Ernesto
2015-01-01
Graph theory provides a useful framework to study functional brain networks from neuroimaging data. In epilepsy research, recent findings suggest that it offers unique insight into the fingerprints of this pathology on brain dynamics. Most studies hitherto have focused on seizure activity during focal epilepsy, but less is known about functional epileptic brain networks during interictal activity in frontal focal and generalized epilepsy. Besides, it is not clear yet which measures are most suitable to characterize these networks. To address these issues, we recorded magnetoencephalographic (MEG) data using two orthogonal planar gradiometers from 45 subjects from three groups (15 healthy controls (7 males, 24 ± 6 years), 15 frontal focal (8 male, 32 ± 16 years) and 15 generalized epileptic (6 male, 27 ± 7 years) patients) during interictal resting state with closed eyes. Then, we estimated the total and relative spectral power of the largest principal component of the gradiometers, and the degree of phase synchronization between each sensor site in the frequency range [0.5-40 Hz]. We further calculated a comprehensive battery of 15 graph-theoretic measures and used the affinity propagation clustering algorithm to elucidate the minimum set of them that fully describe these functional brain networks. The results show that differences in spectral power between the control and the other two groups have a distinctive pattern: generalized epilepsy presents higher total power for all frequencies except the alpha band over a widespread set of sensors; frontal focal epilepsy shows higher relative power in the beta band bilaterally in the fronto-central sensors. Moreover, all network indices can be clustered into three groups, whose exemplars are the global network efficiency, the eccentricity and the synchronizability. Again, the patterns of differences were clear: the brain network of the generalized epilepsy patients presented greater efficiency and lower
What graph theory actually tells us about resting state interictal MEG epileptic activity
Directory of Open Access Journals (Sweden)
Guiomar Niso
2015-01-01
Full Text Available Graph theory provides a useful framework to study functional brain networks from neuroimaging data. In epilepsy research, recent findings suggest that it offers unique insight into the fingerprints of this pathology on brain dynamics. Most studies hitherto have focused on seizure activity during focal epilepsy, but less is known about functional epileptic brain networks during interictal activity in frontal focal and generalized epilepsy. Besides, it is not clear yet which measures are most suitable to characterize these networks. To address these issues, we recorded magnetoencephalographic (MEG data using two orthogonal planar gradiometers from 45 subjects from three groups (15 healthy controls (7 males, 24 ± 6 years, 15 frontal focal (8 male, 32 ± 16 years and 15 generalized epileptic (6 male, 27 ± 7 years patients during interictal resting state with closed eyes. Then, we estimated the total and relative spectral power of the largest principal component of the gradiometers, and the degree of phase synchronization between each sensor site in the frequency range [0.5–40 Hz]. We further calculated a comprehensive battery of 15 graph-theoretic measures and used the affinity propagation clustering algorithm to elucidate the minimum set of them that fully describe these functional brain networks. The results show that differences in spectral power between the control and the other two groups have a distinctive pattern: generalized epilepsy presents higher total power for all frequencies except the alpha band over a widespread set of sensors; frontal focal epilepsy shows higher relative power in the beta band bilaterally in the fronto-central sensors. Moreover, all network indices can be clustered into three groups, whose exemplars are the global network efficiency, the eccentricity and the synchronizability. Again, the patterns of differences were clear: the brain network of the generalized epilepsy patients presented greater
Diestel, Reinhard
2012-01-01
HauptbeschreibungThis standard textbook of modern graph theory, now in its fourth edition, combinesthe authority of a classic with the engaging freshness of style that is the hallmarkof active mathematics. It covers the core material of the subject with concise yetreliably complete proofs, while offering glimpses of more advanced methodsin each field by one or two deeper results, again with proofs given in full detail.The book can be used as a reliable text for an introductory course, as a graduatetext, and for self-study. Rezension"Deep, clear, wonderful. This is a serious book about the
Wallman, Mikael; Smith, Nicolas P; Rodriguez, Blanca
2012-06-01
The bidomain and monodomain equations are well established as the standard set of equations for the simulation of cardiac electrophysiological behavior. However, the computational cost of detailed bidomain/monodomain simulations limits their applicability in scenarios where a large number of simulations needs to be performed (e.g., parameter estimation). In this study, we present a graph-based method, which relies on point-to-point path finding to estimate activation times for single points in cardiac tissue with minimal computational costs. To validate our approach, activation times are compared to monodomain simulation results for an anatomically based rabbit ventricular model, incorporating realistic fiber orientation and conduction heterogeneities. Differences in activation times between the graph-based method and monodomain results are less than 10% of the total activation time, and computational performance is orders of magnitude faster with the proposed method when calculating activation times at single points. These results suggest that the graph-based method is well suited for estimating activation times when the need for fast performance justifies a limited loss of accuracy.
DOF Decoupling Task Graph Model: Reducing the Complexity of Touch-Based Active Sensing
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Niccoló Tosi
2015-05-01
Full Text Available This article presents: (i a formal, generic model for active sensing tasks; (ii the insight that active sensing actions can very often be searched on less than six-dimensional configuration spaces (bringing an exponential reduction in the computational costs involved in the search; (iii an algorithm for selecting actions explicitly trading off information gain, execution time and computational cost; and (iv experimental results of touch-based localization in an industrial setting. Generalizing from prior work, the formal model represents an active sensing task by six primitives: configuration space, information space, object model, action space, inference scheme and action-selection scheme; prior work applications conform to the model as illustrated by four concrete examples. On top of the mentioned primitives, the task graph is then introduced as the relationship to represent an active sensing task as a sequence of low-complexity actions defined over different configuration spaces of the object. The presented act-reason algorithm is an action selection scheme to maximize the expected information gain of each action, explicitly constraining the time allocated to compute and execute the actions. The experimental contributions include localization of objects with: (1 a force-controlled robot equipped with a spherical touch probe; (2 a geometric complexity of the to-be-localized objects up to industrial relevance; (3 an initial uncertainty of (0.4 m, 0.4 m, 2Π; and (4 a configuration of act-reason to constrain the allocated time to compute and execute the next action as a function of the current uncertainty. Localization is accomplished when the probability mass within a 5-mm tolerance reaches a specified threshold of 80%. Four objects are localized with final {mean; standard-deviation} error spanning from {0.0043 m; 0.0034 m} to {0.0073 m; 0.0048 m}.
Sahasranand, K R
2010-01-01
Almost all known secret sharing schemes work on numbers. Such methods will have difficulty in sharing graphs since the number of graphs increases exponentially with the number of nodes. We propose a secret sharing scheme for graphs where we use graph intersection for reconstructing the secret which is hidden as a sub graph in the shares. Our method does not rely on heavy computational operations such as modular arithmetic or polynomial interpolation but makes use of very basic operations like assignment and checking for equality, and graph intersection can also be performed visually. In certain cases, the secret could be reconstructed using just pencil and paper by authorised parties but cannot be broken by an adversary even with unbounded computational power. The method achieves perfect secrecy for (2, n) scheme and requires far fewer operations compared to Shamir's algorithm. The proposed method could be used to share objects such as matrices, sets, plain text and even a heterogeneous collection of these. S...
Zhang, Lei; Zeng, Zhi; Ji, Qiang
2011-09-01
Chain graph (CG) is a hybrid probabilistic graphical model (PGM) capable of modeling heterogeneous relationships among random variables. So far, however, its application in image and video analysis is very limited due to lack of principled learning and inference methods for a CG of general topology. To overcome this limitation, we introduce methods to extend the conventional chain-like CG model to CG model with more general topology and the associated methods for learning and inference in such a general CG model. Specifically, we propose techniques to systematically construct a generally structured CG, to parameterize this model, to derive its joint probability distribution, to perform joint parameter learning, and to perform probabilistic inference in this model. To demonstrate the utility of such an extended CG, we apply it to two challenging image and video analysis problems: human activity recognition and image segmentation. The experimental results show improved performance of the extended CG model over the conventional directed or undirected PGMs. This study demonstrates the promise of the extended CG for effective modeling and inference of complex real-world problems.
Li, Xueliang; Gutman, Ivan
2012-01-01
This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger's result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of g
Comparison of three generations of ActiGraph activity monitors under free-living conditions
DEFF Research Database (Denmark)
Grydeland, May; Hansen, Bjørge Herman; Ried-Larsen, M.
2014-01-01
+ in children in free-living conditions. The generations GT1M and GT3X+ provided comparable outputs. The differences between the old and the newer monitors were more complex when investigating time spent at different intensities. Comparisons of data assessed by the AM7164 with data assessed by newer generations......BACKGROUND: A recent review concludes that the agreement of data across ActiGraph accelerometer models for children and youth still is uncertain. The aim of this study was to evaluate the agreement of three generations of ActiGraph accelerometers in children in a free-living condition. METHODS......: Sixteen 9-year-olds wore the ActiGraph AM7164, GT1M and GT3X+ simultaneously for three consecutive days. We compared mean counts per minute (mcpm) and time spent at different intensities from the three generations of monitors, and the agreement of outputs were evaluated by intra-class correlation...
DEFF Research Database (Denmark)
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
Sun, Min; Chen, Xinjian; Zhang, Zhiqiang; Ma, Chiyuan
2017-02-01
Accurate volume measurements of pituitary adenoma are important to the diagnosis and treatment for this kind of sellar tumor. The pituitary adenomas have different pathological representations and various shapes. Particularly, in the case of infiltrating to surrounding soft tissues, they present similar intensities and indistinct boundary in T1-weighted (T1W) magnetic resonance (MR) images. Then the extraction of pituitary adenoma from MR images is still a challenging task. In this paper, we propose an interactive method to segment the pituitary adenoma from brain MR data, by combining graph cuts based active contour model (GCACM) and random walk algorithm. By using the GCACM method, the segmentation task is formulated as an energy minimization problem by a hybrid active contour model (ACM), and then the problem is solved by the graph cuts method. The region-based term in the hybrid ACM considers the local image intensities as described by Gaussian distributions with different means and variances, expressed as maximum a posteriori probability (MAP). Random walk is utilized as an initialization tool to provide initialized surface for GCACM. The proposed method is evaluated on the three-dimensional (3-D) T1W MR data of 23 patients and compared with the standard graph cuts method, the random walk method, the hybrid ACM method, a GCACM method which considers global mean intensity in region forces, and a competitive region-growing based GrowCut method planted in 3D Slicer. Based on the experimental results, the proposed method is superior to those methods.
Gao, Enting; Shi, Fei; Zhu, Weifang; Jin, Chao; Sun, Min; Chen, Haoyu; Chen, Xinjian
2017-02-01
In this paper, a novel approach combining the active appearance model (AAM) and graph search is proposed to segment retinal layers for optic nerve head(ONH) centered optical coherence tomography(OCT) images. The method includes two parts: preprocessing and layer segmentation. During the preprocessing phase, images is first filtered for denoising, then the B-scans are flattened. During layer segmentation, the AAM is first used to obtain the coarse segmentation results. Then a multi-resolution GS-AAM algorithm is applied to further refine the results, in which AAM is efficiently integrated into the graph search segmentation process. The proposed method was tested on a dataset which contained113-D SD-OCT images, and compared to the manual tracings of two observers on all the volumetric scans. The overall mean border positioning error for layer segmentation was found to be 7.09 +/- 6.18μm for normal subjects. It was comparable to the results of traditional graph search method (8.03+/-10.47μm) and mean inter-observer variability (6.35+/-6.93μm).The preliminary results demonstrated the feasibility and efficiency of the proposed method.
Gomersall, Sjaan R; Ng, Norman; Burton, Nicola W; Pavey, Toby G; Gilson, Nicholas D; Brown, Wendy J
2016-09-07
Activity trackers are increasingly popular with both consumers and researchers for monitoring activity and for promoting positive behavior change. However, there is a lack of research investigating the performance of these devices in free-living contexts, for which findings are likely to vary from studies conducted in well-controlled laboratory settings. The aim was to compare Fitbit One and Jawbone UP estimates of steps, moderate-to-vigorous physical activity (MVPA), and sedentary behavior with data from the ActiGraph GT3X+ accelerometer in a free-living context. Thirty-two participants were recruited using convenience sampling; 29 provided valid data for this study (female: 90%, 26/29; age: mean 39.6, SD 11.0 years). On two occasions for 7 days each, participants wore an ActiGraph GT3X+ accelerometer on their right hip and either a hip-worn Fitbit One (n=14) or wrist-worn Jawbone UP (n=15) activity tracker. Daily estimates of steps and very active minutes were derived from the Fitbit One (n=135 days) and steps, active time, and longest idle time from the Jawbone UP (n=154 days). Daily estimates of steps, MVPA, and longest sedentary bout were derived from the corresponding days of ActiGraph data. Correlation coefficients and Bland-Altman plots with examination of systematic bias were used to assess convergent validity and agreement between the devices and the ActiGraph. Cohen's kappa was used to assess the agreement between each device and the ActiGraph for classification of active versus inactive (≥10,000 steps per day and ≥30 min/day of MVPA) comparable with public health guidelines. Correlations with ActiGraph estimates of steps and MVPA ranged between .72 and .90 for Fitbit One and .56 and .75 for Jawbone UP. Compared with ActiGraph estimates, both devices overestimated daily steps by 8% (Fitbit One) and 14% (Jawbone UP). However, mean differences were larger for daily MVPA (Fitbit One: underestimated by 46%; Jawbone UP: overestimated by 50%). There was
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
DEFF Research Database (Denmark)
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
Diestel, Reinhard
2000-01-01
This book is a concise, yet carefully written, introduction to modern graph theory, covering all its major recent developments. It can be used both as a reliable textbook for an introductory course and as a graduate text: on each topic it covers all the basic material in full detail, and adds one or two deeper results (again with detailed proofs) to illustrate the more advanced methods of that field. This second edition extends the first in two ways. It offers a thoroughly revised and updated chapter on graph minors, which now includes full new proofs of two of the central Robertson-Seymour theorems (as well as a detailed sketch of the entire proof of their celebrated Graph Minor Theorem). Second, there is now a section of hints for all the exercises, to enhance their value for both individual study and classroom use.
Beeken, Paul
2014-11-01
Graphing is an essential skill that forms the foundation of any physical science.1 Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations.2 Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary school instruction, the job of graphing skills falls heavily on physics teachers. By virtue of the nature of the topics we cover, it is our mission to develop this skill to the fine art that it is.
Graphs in Practical Situations
Institute of Scientific and Technical Information of China (English)
刘晓玫; 任心玥
2008-01-01
<正>Linear graphs are often used to depict conversion graphs and travel graphs. Example: The following graph shows the conversion between the Singapore dollar (S $) and the Malay- sian ringgit (RM) in 2000.
Energy Technology Data Exchange (ETDEWEB)
2016-06-01
GraphBench is a benchmark suite for graph pattern mining and graph analysis systems. The benchmark suite is a significant addition to conducting apples-apples comparison of graph analysis software (databases, in-memory tools, triple stores, etc.)
Reddy, A Satyanarayana
2011-01-01
A graph $X$ is said to be a pattern polynomial graph if its adjacency algebra is a coherent algebra. In this study we will find a necessary and sufficient condition for a graph to be a pattern polynomial graph. Some of the properties of the graphs which are polynomials in the pattern polynomial graph have been studied. We also identify known graph classes which are pattern polynomial graphs.
Warchalowski, Wiktor; Krawczyk, Malgorzata J.
2017-03-01
We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.
Betweenness Centrality in Graphs
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such ...
2015-12-31
distribution is unlimited" ES 14. ABSTRACT This report examines the application of factor graphs (graph-based architectures utilizing message passing) to...Research Laboratory The Pennsylvania State University Abstract: This report examines the application of factor graphs (graph-based architectures ...on Particle filtering and Smoothing: Fifteen years later. Tokyo, Japan . Duda, R ., Hart, P ., & Stork, D. (2001). Introduction. In Pattern
Hillman, Thomas
2014-01-01
This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Weinzierl, Stefan
2013-01-01
In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by multiple polylogarithms. The algebraic properties of multiple polylogarithms are reviewed in the second part of these lectures. The final part of these lectures is devoted to Feynman integrals, which cannot be expressed in terms of multiple polylogarithms. Methods from algebraic geometry provide tools to tackle these integrals.
Learning Mathematics with Interactive Whiteboards and Computer-Based Graphing Utility
Erbas, Ayhan Kursat; Ince, Muge; Kaya, Sukru
2015-01-01
The purpose of this study was to explore the effect of a technology-supported learning environment utilizing an interactive whiteboard (IWB) and NuCalc graphing software compared to a traditional direct instruction-based environment on student achievement in graphs of quadratic functions and attitudes towards mathematics and technology. Sixty-five…
Hekler, Eric B; Buman, Matthew P; Grieco, Lauren; Rosenberger, Mary; Winter, Sandra J; Haskell, William; King, Abby C
2015-04-15
There is increasing interest in using smartphones as stand-alone physical activity monitors via their built-in accelerometers, but there is presently limited data on the validity of this approach. The purpose of this work was to determine the validity and reliability of 3 Android smartphones for measuring physical activity among midlife and older adults. A laboratory (study 1) and a free-living (study 2) protocol were conducted. In study 1, individuals engaged in prescribed activities including sedentary (eg, sitting), light (sweeping), moderate (eg, walking 3 mph on a treadmill), and vigorous (eg, jogging 5 mph on a treadmill) activity over a 2-hour period wearing both an ActiGraph and 3 Android smartphones (ie, HTC MyTouch, Google Nexus One, and Motorola Cliq). In the free-living study, individuals engaged in usual daily activities over 7 days while wearing an Android smartphone (Google Nexus One) and an ActiGraph. Study 1 included 15 participants (age: mean 55.5, SD 6.6 years; women: 56%, 8/15). Correlations between the ActiGraph and the 3 phones were strong to very strong (ρ=.77-.82). Further, after excluding bicycling and standing, cut-point derived classifications of activities yielded a high percentage of activities classified correctly according to intensity level (eg, 78%-91% by phone) that were similar to the ActiGraph's percent correctly classified (ie, 91%). Study 2 included 23 participants (age: mean 57.0, SD 6.4 years; women: 74%, 17/23). Within the free-living context, results suggested a moderate correlation (ie, ρ=.59, PAndroid smartphone can provide comparable estimates of physical activity to an ActiGraph in both a laboratory-based and free-living context for estimating sedentary and MVPA and that different Android smartphones may reliably confer similar estimates.
Merris, Russell
2001-01-01
A lively invitation to the flavor, elegance, and power of graph theoryThis mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. An award-winning teacher, Russ Merris has crafted a book designed to attract and engage through its spirited exposition, a rich assortment of well-chosen exercises, and a selection of topics that emphasizes the kinds of things that can be manipulated, counted, and pictured. Intended neither to be a comprehensive overview nor an encyclopedic reference, th
Technology-Supported Learning Environments in Science Classrooms in India
Gupta, Adit; Fisher, Darrell
2012-01-01
The adoption of technology has created a major impact in the field of education at all levels. Technology-supported classroom learning environments, involving modern information and communication technologies, are also entering the Indian educational system in general and the schools in Jammu region (Jammu & Kashmir State, India) in particular.…
The Elusive Benefits of the Technological Support of Knowledge Management.
Flanagin, Andrew J.
2002-01-01
Considers the application of technological tools to knowledge management and the difficulties and developments in the technological support of knowledge management. Hopes to capture the tacit knowledge of experienced organizational members, make it more explicit in the form of simulation scenarios, and to turn it into tacit knowledge for trainees…
Internationalization at home : Technology-supported multicultural learning in Peru
Olivos Rossini, L.M.
2016-01-01
This research contributes to the disciplines of information systems, management science in particular the field of management education and cross-cultural studies. It further proposes a model to understand technology-supported multicultural learning in Peru. In addition, the model examines intercult
Exploring Technology Supported Collaborative and Cooperative Group Formation Mechanisms
Carapina, Mia; Boticki, Ivica
2015-01-01
This paper reflects on the systematic literature review paper (in progress), which analyzes technology enhanced collaborative and cooperative learning in elementary education worldwide from 2004 to 2015, focusing on the exploration of technology mediated group formation. The review paper reports on only a few cases of technology supported methods…
Technology-Supported Learning Environments in Science Classrooms in India
Gupta, Adit; Fisher, Darrell
2012-01-01
The adoption of technology has created a major impact in the field of education at all levels. Technology-supported classroom learning environments, involving modern information and communication technologies, are also entering the Indian educational system in general and the schools in Jammu region (Jammu & Kashmir State, India) in…
Understanding Graphs & Charts.
Cleary, John J.; Gravely, Mary Liles
Developed by educators from the Emily Griffith Opportunity School, this teacher's guide was developed for a 4-hour workshop to teach employees how to read the charts and graphs they need in the workplace. The unit covers four types of graphs: pictographs, bar graphs, line graphs, and circle graphs. The guide is divided into four sections: reading…
Directory of Open Access Journals (Sweden)
Hiroyuki Akama
Full Text Available In this study, we introduce an original distance definition for graphs, called the Markov-inverse-F measure (MiF. This measure enables the integration of classical graph theory indices with new knowledge pertaining to structural feature extraction from semantic networks. MiF improves the conventional Jaccard and/or Simpson indices, and reconciles both the geodesic information (random walk and co-occurrence adjustment (degree balance and distribution. We measure the effectiveness of graph-based coefficients through the application of linguistic graph information for a neural activity recorded during conceptual processing in the human brain. Specifically, the MiF distance is computed between each of the nouns used in a previous neural experiment and each of the in-between words in a subgraph derived from the Edinburgh Word Association Thesaurus of English. From the MiF-based information matrix, a machine learning model can accurately obtain a scalar parameter that specifies the degree to which each voxel in (the MRI image of the brain is activated by each word or each principal component of the intermediate semantic features. Furthermore, correlating the voxel information with the MiF-based principal components, a new computational neurolinguistics model with a network connectivity paradigm is created. This allows two dimensions of context space to be incorporated with both semantic and neural distributional representations.
Tan, Yong
2013-01-01
In this paper, author uses set theory to construct a logic model of abstract figure from binary relation. Based on the uniform quantified structure, author gives two logic system for graph traversal and graph coloring respectively, moreover shows a new method of cutting graph. Around this model, there are six algorithms in this paper including exact graph traversal, Algebra calculation of natural number, graph partition and graph coloring.
A Study of Science and Technology Support System for Multifunctional Forestry
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Based on the analysis on existing problems in China's forestry science & technology support system and in view of the requirements of multifunctional forestry development for science & technology support, the paper constructed a science & technology support framework for multifunctional forestry, comprising technology innovation, achievements transfer, extension and application, and policy guarantee. Major countermeasures were proposed to consolidate the science & technology support to multifunctional fores...
Attitudes of Teacher Candidates Towards Technology Supported Collaborative Learning
Directory of Open Access Journals (Sweden)
Fezile ÖZDAMLI
2008-06-01
Full Text Available Technology supported collaborative learning allows students to study together, and produce projectstogether using technology supported systems. This study aimed to gather attitudes of CEIT students’ in the matter oftechnology supported collaborative learning in the Near East University. Pre-experimental model used in this study. Datawere collected from the students at the start of the term and end. This study was applied to selected sample of 35 students (24male and 11 females of Computer Education and Instructional Technologies Department of Near East University and whogot the course “authorware tools” at the 1St term of 2007-2008 academic year. The participants got the course “authoringtools application in computer enviorment” which was carried out as a technology supported collaborative learning. Thetechnology supported collaborative learning and authoring tools were described to students by teachers at the begining of theterm. Each team has 2 or 3 members. Teams selected projects topics at the begining of term. The aim of the final projects wascreated a course software about their project topics. Students were discussed the topics with team members and researced thetopics then they created a course software. The course included a series of local face-to-face tutorials (four each week duringa term and was supported by e-mail, msn, and discussion forums in a website. Teachers and student teams were discussedthe topics and projects during terms and then presented their projects. “the role of the technology on the course” and“Adaptation to the collaborative learning criters” 5 point likert scales and “personal information forums” were used in thisstudy. The results were generally positive at the start and at the end of the term. Besides, students’ attidues were morepositive than after studying in technology supported collaborative learning.
Semantic graphs and associative memories.
Pomi, Andrés; Mizraji, Eduardo
2004-12-01
Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.
Directory of Open Access Journals (Sweden)
Juan eNunez-Iglesias
2014-04-01
Full Text Available The aim in high-resolution connectomics is to reconstruct complete neuronal connectivity in a tissue. Currently, the only technology capable of resolving the smallest neuronal processes is electron microscopy (EM. Thus, a common approach is to perform automatic segmentation of EM images, followed by manual proofreading by experts to fix errors. We developed an algorithm and software library to not only improve the accuracy of the initial automatic segmentation, but also point out the image coordinates where it is likely to have made errors. Our software, called gala (graph-based active learning of agglomeration, improves the state of the art in agglomerative image segmentation. It is implemented in Python and makes extensive use of the scientific Python stack (numpy, scipy, networkx, scikit-learn, scikit-image, and others. We present here the software architecture of the gala library, and discuss several designs that we consider would be generally useful for other segmentation packages. We also discuss the limitations of the gala library and how we intend to address them.
Nunez-Iglesias, Juan; Kennedy, Ryan; Plaza, Stephen M; Chakraborty, Anirban; Katz, William T
2014-01-01
The aim in high-resolution connectomics is to reconstruct complete neuronal connectivity in a tissue. Currently, the only technology capable of resolving the smallest neuronal processes is electron microscopy (EM). Thus, a common approach to network reconstruction is to perform (error-prone) automatic segmentation of EM images, followed by manual proofreading by experts to fix errors. We have developed an algorithm and software library to not only improve the accuracy of the initial automatic segmentation, but also point out the image coordinates where it is likely to have made errors. Our software, called gala (graph-based active learning of agglomeration), improves the state of the art in agglomerative image segmentation. It is implemented in Python and makes extensive use of the scientific Python stack (numpy, scipy, networkx, scikit-learn, scikit-image, and others). We present here the software architecture of the gala library, and discuss several designs that we consider would be generally useful for other segmentation packages. We also discuss the current limitations of the gala library and how we intend to address them.
Laws, Priscilla
2010-02-01
In June 1986 Ronald Thornton (at the Tufts University Center for Science and Mathematics Teaching) and Priscilla Laws (at Dickinson College) applied independently for grants to develop curricular materials based on both the outcomes of Physics Education Research and the use of Microcomputer Based Laboratory Tools (MBL) developed by Robert Tinker, Ron Thornton and others at Technical Education Research Centers (TERC). Thornton proposed to develop a series of Tools for Scientific Thinking (TST) laboratory exercises to address known learning difficulties using carefully sequenced MBL observations. These TST laboratories were to be beta tested at several types of institutions. Laws proposed to develop a Workshop Physics Activity Guide for a 2 semester calculus-based introductory course sequence centering on MBL-based guided inquiry. Workshop Physics was to be designed to replace traditional lectures and separate labs in relatively small classes and was to be tested at Dickinson College. In September 1986 a project officer at the Fund for Post-Secondary Education (FIPSE) awarded grants to Laws and Thornton provided that they would collaborate. David Sokoloff (at the University of Oregon) joined Thornton to develop and test the TST laboratories. This talk will describe the 23 year collaboration between Thornton, Laws, and Sokoloff that led to the development of a suite of Activity Based Physics curricular materials, new apparatus and enhanced computer tools for real time graphing, data collection and mathematical modeling. The Suite includes TST Labs, the Workshop Physics Activity Guide, RealTime Physics Laboratory Modules, and a series of Interactive Lecture Demonstrations. A textbook and a guide to using the Suite were also developed. The vital importance of obtaining continued grant support, doing continuous research on student learning, collaborating with instructors at other institutions, and forging relationships with vendors and publishers will be described. )
Lawes, Jonathan F.
2013-01-01
Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…
2014-01-01
© 2015 Elsevier B.V. Motivated by recent extensive studies on Wenger graphs, we introduce a new infinite class of bipartite graphs of a similar type, called linearized Wenger graphs. The spectrum, diameter and girth of these linearized Wenger graphs are determined.
Shao, Zheng; Hirayama, Yuya; Yamanishi, Yoshihiro; Saigo, Hiroto
2015-12-28
Graph data are becoming increasingly common in machine learning and data mining, and its application field pervades to bioinformatics and cheminformatics. Accordingly, as a method to extract patterns from graph data, graph mining recently has been studied and developed rapidly. Since the number of patterns in graph data is huge, a central issue is how to efficiently collect informative patterns suitable for subsequent tasks such as classification or regression. In this paper, we consider mining discriminative subgraphs from graph data with multiple labels. The resulting task has important applications in cheminformatics, such as finding common functional groups that trigger multiple drug side effects, or identifying ligand functional groups that hit multiple targets. In computational experiments, we first verify the effectiveness of the proposed approach in synthetic data, then we apply it to drug adverse effect prediction problem. In the latter dataset, we compared the proposed method with L1-norm logistic regression in combination with the PubChem/Open Babel fingerprint, in that the proposed method showed superior performance with a much smaller number of subgraph patterns. Software is available from https://github.com/axot/GLP.
The trends in technology supported collaborative learning studies in 21st century
Directory of Open Access Journals (Sweden)
Hafize Keser, Huseyin Uzunboylu, Fezile Ozdamli
2011-08-01
Full Text Available Technology supported collaborative learning, assists individuals to work as a team for a common purpose or mission by using computer, internet and such technologies. For a common mission, active learning should be provided by applying collaborative learning approach. A lot of studies had been done with using collaborative learning. In order to learn the effectiveness of collaborative learning, a variety of studies and techniques should be prepared. Collaborative learning studies support individuals to be learners for a life time. Besides, there exist considerable numbers of studies that were done on the techniques of technology supported collaborative learning. In significant proportion of the presented studies, the online systems have been introduced that were developed for technology supported collaborative learning. In literature, meta-analysis studies were also found related to collaborative learning methods (Jigsaw etc.. When the literature is examined a lot of studies are found related to the particular subject however, there do not exist any recent made researches on the trends of this topic. The main purpose of this study is to determine new trends for those who aim to make research in technology supported collaborative learning, published in popular magazines in the field of education technology between the years 2005 and 2010. Four journals had been chosen in the study to be identified within the scope of SSCI from EBSCO database. 114 studies have been attained after the scan made on SSCI covered journals published between the years 2005 and 2010. The reporting of the study was grouped according to following criteria; publishing year of the finding, article number (of the journals, number of authors, research field, techniques, study environment, research country (sampling group, study model, number of references, researchers’ county, the number of studies made with the researchers from different countries, type of the study
CUDA Enabled Graph Subset Examiner
Energy Technology Data Exchange (ETDEWEB)
2016-12-22
Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k vertices with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Directory of Open Access Journals (Sweden)
C. Dalfo
2015-10-01
Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.
Spectral recognition of graphs
Directory of Open Access Journals (Sweden)
Cvetković Dragoš
2012-01-01
Full Text Available At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs were found. Still some graphs are characterized by their spectra and several mathematical papers are devoted to this topic. In applications to computer sciences, spectral graph theory is considered as very strong. The benefit of using graph spectra in treating graphs is that eigenvalues and eigenvectors of several graph matrices can be quickly computed. Spectral graph parameters contain a lot of information on the graph structure (both global and local including some information on graph parameters that, in general, are computed by exponential algorithms. Moreover, in some applications in data mining, graph spectra are used to encode graphs themselves. The Euclidean distance between the eigenvalue sequences of two graphs on the same number of vertices is called the spectral distance of graphs. Some other spectral distances (also based on various graph matrices have been considered as well. Two graphs are considered as similar if their spectral distance is small. If two graphs are at zero distance, they are cospectral. In this sense, cospectral graphs are similar. Other spectrally based measures of similarity between networks (not necessarily having the same number of vertices have been used in Internet topology analysis, and in other areas. The notion of spectral distance enables the design of various meta-heuristic (e.g., tabu search, variable neighbourhood search algorithms for constructing graphs with a given spectrum (spectral graph reconstruction. Several spectrally based pattern recognition problems appear in many areas (e.g., image segmentation in computer vision, alignment of protein-protein interaction networks in bio
Pancyclic and bipancyclic graphs
George, John C; Wallis, W D
2016-01-01
This book is focused on pancyclic and bipancyclic graphs and is geared toward researchers and graduate students in graph theory. Readers should be familiar with the basic concepts of graph theory, the definitions of a graph and of a cycle. Pancyclic graphs contain cycles of all possible lengths from three up to the number of vertices in the graph. Bipartite graphs contain only cycles of even lengths, a bipancyclic graph is defined to be a bipartite graph with cycles of every even size from 4 vertices up to the number of vertices in the graph. Cutting edge research and fundamental results on pancyclic and bipartite graphs from a wide range of journal articles and conference proceedings are composed in this book to create a standalone presentation. The following questions are highlighted through the book: - What is the smallest possible number of edges in a pancyclic graph with v vertices? - When do pancyclic graphs exist with exactly one cycle of every possible length? - What is the smallest possible number of...
Yap, Hian-Poh
1996-01-01
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.
Graph algorithms in the titan toolkit.
Energy Technology Data Exchange (ETDEWEB)
McLendon, William Clarence, III; Wylie, Brian Neil
2009-10-01
Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.
National Research Council Canada - National Science Library
Compeau, Phillip E.C
2011-01-01
We consider four families of pancake graphs, which are Cayley graphs, whose vertex sets are either the symmetric group on n objects or the hyperoctahedral group on n objects and whose generating sets...
2013-01-01
on Facebook , one would like to detect tightly connected communities, which is useful for subsequent tasks like customized recommendation and... advertisement . Graphs in modern applications have several characteristics that complicate graph clustering: • Small density gap: the edge density across
Shuai, Hong-Han; Yu, Philip S; Shen, Chih-Ya; Chen, Ming-Syan
2013-01-01
The importance of graph mining has been widely recognized thanks to a large variety of applications in many areas, while real datasets always play important roles to examine the solution quality and efficiency of a graph mining algorithm. Nevertheless, the size of a real dataset is usually fixed and constrained according to the available resources, such as the efforts to crawl an on-line social network. In this case, employing a synthetic graph generator is a possible way to generate a massive graph (e.g., billions nodes) for evaluating the scalability of an algorithm, and current popular statistical graph generators are properly designed to maintain statistical metrics such as total node degree, degree distribution, diameter, and clustering coefficient of the original social graphs. Nevertheless, in addition to the above metrics, recent studies on graph mining point out that graph frequent patterns are also important to provide useful implications for the corresponding social networking applications, but thi...
Evolutionary Graph Drawing Algorithms
Institute of Scientific and Technical Information of China (English)
Huang Jing-wei; Wei Wen-fang
2003-01-01
In this paper, graph drawing algorithms based on genetic algorithms are designed for general undirected graphs and directed graphs. As being shown, graph drawing algorithms designed by genetic algorithms have the following advantages: the frames of the algorithms are unified, the method is simple, different algorithms may be attained by designing different objective functions, therefore enhance the reuse of the algorithms. Also, aesthetics or constrains may be added to satisfy different requirements.
On molecular graph comparison.
Melo, Jenny A; Daza, Edgar
2011-06-01
Since the last half of the nineteenth century, molecular graphs have been present in several branches of chemistry. When used for molecular structure representation, they have been compared after mapping the corresponding graphs into mathematical objects. However, direct molecular comparison of molecular graphs is a research field less explored. The goal of this mini-review is to show some distance and similarity coefficients which were proposed to directly compare molecular graphs or which could be useful to do so.
Integral trees and integral graphs
Wang, Ligong
2005-01-01
This monograph deals with integral graphs, Laplacian integral regular graphs, cospectral graphs and cospectral integral graphs. The organization of this work, which consists of eight chapters, is as follows.
Ellens, W.; Spieksma, F.M.; Mieghem, P. van; Jamakovic, A.; Kooij, R.E.
2011-01-01
This paper studies an interesting graph measure that we call the effective graph resistance. The notion of effective graph resistance is derived from the field of electric circuit analysis where it is defined as the accumulated effective resistance between all pairs of vertices. The objective of the
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Directory of Open Access Journals (Sweden)
Charles Suffel
1982-01-01
Full Text Available A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian.
Loukas, A.
2015-01-01
We have recently seen a surge of research focusing on the processing of graph data. The emerging field of signal processing on graphs focuses on the extension of classical discrete signal processing techniques to the graph setting. Arguably, the greatest breakthrough of the field has been the extens
Teaching Discrete Mathematics with Graphing Calculators.
Masat, Francis E.
Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and…
Yoder, Sharon K.
This book discusses four kinds of graphs that are taught in mathematics at the middle school level: pictographs, bar graphs, line graphs, and circle graphs. The chapters on each of these types of graphs contain information such as starting, scaling, drawing, labeling, and finishing the graphs using "LogoWriter." The final chapter of the book…
Gross, Jonathan L
2003-01-01
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as ""pure"" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to fi
Wong, Pak C.; Mackey, Patrick S.; Perrine, Kenneth A.; Foote, Harlan P.; Thomas, James J.
2008-12-23
Methods for visualizing a graph by automatically drawing elements of the graph as labels are disclosed. In one embodiment, the method comprises receiving node information and edge information from an input device and/or communication interface, constructing a graph layout based at least in part on that information, wherein the edges are automatically drawn as labels, and displaying the graph on a display device according to the graph layout. In some embodiments, the nodes are automatically drawn as labels instead of, or in addition to, the label-edges.
Directory of Open Access Journals (Sweden)
Bonnie J. Spring
2016-08-01
Full Text Available Purpose: Less time spent in sedentary behaviors is associated with improved health and disease outcomes in breast cancer survivors. However, little is known about survivors’ interest in sedentary behavior reduction interventions and how to effectively reduce this risk behavior. The purpose of this study was to explore breast cancer survivors’ interest in and preferences for technology-supported sedentary behavior reduction interventions. Methods: Breast cancer survivors (n = 279; Mage = 60.7 (SD = 9.7 completed a battery of online questionnaires. Descriptive statistics were calculated for all data. To examine potential relationships between demographic, disease and behavioral factors, and survivors’ interest in a technology-supported sedentary behavior reduction intervention, we conducted logistic regression analyses. These same factors were examined in relation to the perceptions of the effectiveness of such intervention using multiple regression analyses. Results: On average, survivors spent 10.1 (SD = 4.3 hours/day in sedentary activity. They believed prolonged periods of sedentary behavior were harmful to their health (87.0% and that reducing sedentary behavior could improve their health (88.4%. Survivors believed they should move around after 30–60 (56.7% or ≥ 60 (29.9% minutes of sedentary behavior and indicated they were most likely to replace sedentary behaviors with walking around (97.1% or walking in place (73.4%. The majority of survivors (79.9% was interested in participating in a technology-supported sedentary behavior reduction intervention and indicated they would use a smartphone application (61.3% 2–3 times/day (48.0%, 6 to 7 days/week (52.0%. Most survivors (73.5% believed reminders would help them decrease sedentary behavior and preferred they be delivered after sitting for 60 minutes (60.5% via vibrations on a wrist worn activity tracker (77.3% or text messages (54.4%. Conclusions: Technology-supported sedentary
Caetano, Tiberio S; Cheng, Li; Le, Quoc V; Smola, Alex J
2008-01-01
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the `labels' are ma...
Harrison, JM; Robbins, JM; 10.1098/rspa.2010.0254
2011-01-01
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molec...
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Jampani, Krishnam Raju
2010-01-01
In a recent paper, we introduced the simultaneous representation problem (defined for any graph class C) and studied the problem for chordal, comparability and permutation graphs. For interval graphs, the problem is defined as follows. Two interval graphs G_1 and G_2, sharing some vertices I (and the corresponding induced edges), are said to be `simultaneous interval graphs' if there exist interval representations R_1 and R_2 of G_1 and G_2, such that any vertex of I is mapped to the same interval in both R_1 and R_2. Equivalently, G_1 and G_2 are simultaneous interval graphs if there exist edges E' between G_1-I and G_2-I such that G_1 \\cup G_2 \\cup E' is an interval graph. Simultaneous representation problems are related to simultaneous planar embeddings, and have applications in any situation where it is desirable to consistently represent two related graphs, for example: interval graphs capturing overlaps of DNA fragments of two similar organisms; or graphs connected in time, where one is an updated versi...
O'Brien, O A; McCarthy, M; Gibney, E R; McAuliffe, F M
2014-07-01
Overweight and obesity are associated with increased risk of adverse maternal and fetal outcomes. However, the actuality of delivering effective lifestyle interventions in clinical practice is hampered by a high demand for resources. The use of technology to assist lifestyle interventions needs to be explored as a valid method of reducing strain on resources, and enhancing the effectiveness and population reach of interventions. The aim was to systematically review the literature on the use of technology-supported lifestyle interventions for healthy pregnant women and their impact on maternal outcomes. Online databases and registries were searched in March 2013. Primary outcomes of selected English language studies were fasting maternal glucose, incidence of gestational diabetes mellitus (GDM) and maternal gestational weight gain. Secondary outcomes were intervention uptake and acceptance, and dietary or physical activity modification. Studies whose subjects were diagnosed with GDM prior to intervention were excluded. The minimal number of eligible studies and varying outcomes precluded formal meta-analysis of the data. Initially, 203 articles were identified and screened. Seven articles, including five randomised controlled trials, met inclusion criteria for the current review. Results demonstrate several potential benefits associated with technology-supported interventions in pregnancy, despite minimal search results. Although communication technology holds potential as a safe therapeutic tool for the support of lifestyle interventions in pregnancy, there is a paucity of data on its effectiveness. Further RCTs examining the effectiveness of communication technology are required, particularly among those most likely to benefit from lifestyle interventions, such as overweight and obese pregnant women.
Fujie, Futaba
2014-01-01
Covering Walks in Graphs is aimed at researchers and graduate students in the graph theory community and provides a comprehensive treatment on measures of two well studied graphical properties, namely Hamiltonicity and traversability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known mathematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamiltonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relationship between traceable concepts and...
Dosen, K
2011-01-01
Plural (or multiple-conclusion) cuts are inferences made by applying a structural rule introduced by Gentzen for his sequent formulation of classical logic. As singular (single-conclusion) cuts yield trees, which underlie ordinary natural deduction derivations, so plural cuts yield graphs of a more complicated kind, related to trees, which this paper defines. Besides the inductive definition of these oriented graphs, which is based on sequent systems, a non-inductive, graph-theoretical, combinatorial, definition is given, and to reach that other definition is the main goal of the paper. As trees underlie multicategories, so the graphs of plural cuts underlie polycategories. The graphs of plural cuts are interesting in particular when the plural cuts are appropriate for sequent systems without the structural rule of permutation, and the main body of the paper deals with that matter. It gives a combinatorial characterization of the planarity of the graphs involved.
Velasco, Pedro Pablo Perez
2008-01-01
This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.
Arrighi, Pablo
2012-01-01
We generalize the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph. The notion of translation-invariance is also generalized. The definition we provide for these `causal graph dynamics' is simple and axiomatic. The theorems we provide also show that it is robust. For instance, causal graph dynamics are stable under composition and under restriction to radius one. In the finite case some fundamental facts of Cellular Automata theory carry through: causal graph dynamics admit a characterization as continuous functions and they are stable under inversion. The provided examples suggest a wide range of applications of this mathematical object, from complex systems science to theoretical physics. Keywords: Dynamical networks, Boolean network...
Buczyńska, Weronika
2010-01-01
We define toric projective model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. Generators of the projective coordinate ring of the models of graphs with one cycle are explicitly described. The models of graphs with the same topological invariants are deformation equivalent and share the same Hilbert function. We also provide an algorithm to compute the Hilbert function.
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Energy Technology Data Exchange (ETDEWEB)
Lothian, Josh [ORNL; Powers, Sarah S [ORNL; Sullivan, Blair D [ORNL; Baker, Matthew B [ORNL; Schrock, Jonathan [ORNL; Poole, Stephen W [ORNL
2013-12-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of dierent application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
DEFF Research Database (Denmark)
Thomassen, Carsten
2014-01-01
We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k.......We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k....
Gelfand, I M; Shnol, E E
2002-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Bradford, Robert; Chmutov, Sergei
2011-01-01
We introduce an additional structure on ribbon graphs, arrow structure. We extend the Bollob\\'as-Riordan polynomial to ribbon graph with this structure. The extended polynomial satisfies the contraction-deletion relations and naturally behaves with respect to the partial duality of ribbon graphs. We construct an arrow ribbon graph from a virtual link whose extended Bollob\\'as-Riordan polynomial specializes to the arrow polynomial of the virtual link recently introduced by H.Dye and L.Kauffman. This result generalizes the classical Thistlethwaite theorem to the arrow polynomial of virtual links.
Directory of Open Access Journals (Sweden)
Alberto Apostolico
2009-08-01
Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.
Institute of Scientific and Technical Information of China (English)
Ping WANG; Jiong Sheng LI
2005-01-01
Let G be a finite simple graph with adjacency matrix A, and let P(A) be the convex closure of the set of all permutation matrices commuting with A. G is said to be compact if every doubly stochastic matrix which commutes with A is in P(A). In this paper, we characterize 3-regular compact graphs and prove that if G is a connected regular compact graph, G - v is also compact, and give a family of almost regular compact connected graphs.
Framings for graph hypersurfaces
Brown, Francis
2013-01-01
We present a method for computing the framing on the cohomology of graph hypersurfaces defined by the Feynman differential form. This answers a question of Bloch, Esnault and Kreimer in the affirmative for an infinite class of graphs for which the framings are Tate motives. Applying this method to the modular graphs of Brown and Schnetz, we find that the Feynman differential form is not of Tate type in general. This finally disproves a folklore conjecture stating that the periods of Feynman integrals of primitive graphs in phi^4 theory factorise through a category of mixed Tate motives.
Caetano, Tibério S; McAuley, Julian J; Cheng, Li; Le, Quoc V; Smola, Alex J
2009-06-01
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.
Rensink, Arend; Distefano, Dino
2005-01-01
Graphs may be used as representations of system states in operational semantics and model checking; in the latter context, they are being investigated as an alternative to bit vectors. The corresponding transitions are obtained as derivations from graph production rules. In this paper we propose an
Rensink, Arend; Distefano, Dino; Mukhopadhyay, S.; Roychoudhury, A.; Yang, Z.
2006-01-01
Graphs may be used as representations of system states in operational semantics and model checking; in the latter context, they are being investigated as an alternative to bit vectors. The corresponding transitions are obtained as derivations from graph production rules. In this paper we propose an
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...
DEFF Research Database (Denmark)
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Directory of Open Access Journals (Sweden)
Behnaz Tolue
2018-07-01
Full Text Available In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1\\cap H_2\
Mol, de Maarten; Rensink, Arend; Hunt, James J.
2012-01-01
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class declaration
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available techniques and is organized by algorithmic paradigm.
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems i
Belkhechine, Houmem; Elayech, Mohamed Baka
2010-01-01
Given a (directed) graph G=(V,A), a subset X of V is an interval of G provided that for any a, b\\in X and x\\in V-X, (a,x)\\in A if and only if (b,x)\\in A and (x,a)\\in A if and only if (x,b)\\in A. For example, \\emptyset, \\{x\\} (x \\in V) and V are intervals of G, called trivial intervals. A graph, all the intervals of which are trivial, is indecomposable; otherwise, it is decomposable. A vertex x of an indecomposable graph is critical if G-x is decomposable. In 1993, J.H. Schmerl and W.T. Trotter characterized the indecomposable graphs, all the vertices of which are critical, called critical graphs. In this article, we characterize the indecomposable graphs which admit a single non critical vertex, that we call (-1)-critical graphs.} This gives an answer to a question asked by Y. Boudabbous and P. Ille in a recent article studying the critical vertices in an indecomposable graph.
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A. Assari
2016-01-01
Full Text Available In this paper, a graph is assigned to any probability measure on the σ-algebra of Borel sets of a topological space. Using this construction, it is proved that given any number n (finite or infinite there exists a nonregular graph such that its clique, chromatic, and dominating number equals n.
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...... algebras and of simple algebraic groups. The first section contains some background on equivariant cohomology....
Graphs: Associated Markov Chains
2012-01-01
In this research paper, weighted / unweighted, directed / undirected graphs are associated with interesting Discrete Time Markov Chains (DTMCs) as well as Continuous Time Markov Chains (CTMCs). The equilibrium / transient behaviour of such Markov chains is studied. Also entropy dynamics (Shannon entropy) of certain structured Markov chains is investigated. Finally certain structured graphs and the associated Markov chains are studied.
Kim, Suh-Ryung; Park, Boram; Sano, Yoshio
2011-01-01
The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x,v)$ and $(y,v)$ are arcs of $D$. For any graph $G$, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ of $G$ is the smallest number of such isolated vertices. In general, it is hard to compute the competition number $k(G)$ for a graph $G$ and it has been one of the important research problems in the study of competition graphs. Opsut~[1982] suggested that the edge clique cover number $\\theta_E(G)$ should be closely related to $k(G)$ by showing $\\theta_E(G)-|V(G)|+2 \\leq k(G) \\leq \\theta_E(G)$. In this note, we study on these inequalities. We first show that for any positive integer $m$ satisfying $2 \\leq m \\leq |V(G)|$, there is a graph $G$ satisfying $k(G)=\\theta_E(G)-|V(G)|+m$ and characterize a graph $G$ satisfying $k(G)=\\...
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Cakula, Sarma
2011-01-01
Problem-based learning and technology support for students in higher education investigates the new perspectives of education in connection with the change of life paradigm. The present research seeks to find out what study methods and technology support can be used for developing students' creative experience in the context of education for…
Chen, Xinjian; Udupa, Jayaram K; Alavi, Abass; Torigian, Drew A
2013-05-01
Image segmentation methods may be classified into two categories: purely image based and model based. Each of these two classes has its own advantages and disadvantages. In this paper, we propose a novel synergistic combination of the image based graph-cut (GC) method with the model based ASM method to arrive at the GC-ASM method for medical image segmentation. A multi-object GC cost function is proposed which effectively integrates the ASM shape information into the GC framework. The proposed method consists of two phases: model building and segmentation. In the model building phase, the ASM model is built and the parameters of the GC are estimated. The segmentation phase consists of two main steps: initialization (recognition) and delineation. For initialization, an automatic method is proposed which estimates the pose (translation, orientation, and scale) of the model, and obtains a rough segmentation result which also provides the shape information for the GC method. For delineation, an iterative GC-ASM algorithm is proposed which performs finer delineation based on the initialization results. The proposed methods are implemented to operate on 2D images and evaluated on clinical chest CT, abdominal CT, and foot MRI data sets. The results show the following: (a) An overall delineation accuracy of TPVF > 96%, FPVF segmentation step compared to GC which requires seed specification and improves on the accuracy of GC. (e) One disadvantage of GC-ASM is its increased computational expense owing to the iterative nature of the algorithm.
Graph-theoretical concepts and physicochemical data
Directory of Open Access Journals (Sweden)
Lionello Pogliani
2003-02-01
Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.
Directory of Open Access Journals (Sweden)
Niedzialomski Amanda
2016-11-01
Full Text Available For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u − f(v| ≥ k + 1 − d(u, v. We consider k-radio labelings of G when k = diam(G. In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio graceful Hamming graphs. The main result shows that the Cartesian product of t copies of a complete graph is radio graceful for certain t. Graphs of this form provide infinitely many examples of radio graceful graphs of arbitrary diameter. We also show that these graphs are not radio graceful for large t.
Bidimensionality and Geometric Graphs
Fomin, Fedor V; Saurabh, Saket
2011-01-01
In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead exhibit a geometric structure. In particular we present EPTASs and subexponential time parameterized algorithms for Feedback Vertex Set, Vertex Cover, Connected Vertex Cover, Diamond Hitting Set, on map graphs and unit disk graphs, and for Cycle Packing and Minimum-Vertex Feedback Edge Set on unit disk graphs. Our results are based on the recent decomposition theorems proved by Fomin et al [SODA 2011], and our algorithms work directly on the input graph. Thus it is not necessary to compute the geometric representations of the input graph. To the best of our knowledge, these results are previously unknown, with the exception of the EPTAS and a subexponential time parameterized algorithm on unit disk graphs for Vertex Cover, which were obtained by Marx [ESA 2005] and Alber and...
An exploratory study of engagement in a technology-supported substance abuse intervention
Directory of Open Access Journals (Sweden)
VanDeMark Nancy R
2010-06-01
Full Text Available Abstract Background The continuing gap between the number of people requiring treatment for substance use disorders and those receiving treatment suggests the need to develop new approaches to service delivery. Meanwhile, the use of technology to provide counseling and support in the substance abuse field is exploding. Despite the increase in the use of technology in treatment, little is known about the impact of technology-supported interventions on access to services for substance use disorders. The E-TREAT intervention brings together the evidence-based practice of Motivational Interviewing and theories of Persuasive Technology to sustain clients' motivation to change substance use behaviors, provide support for change, and facilitate continuity across treatment settings. Methods This study used descriptive statistics, tests of statistical significance, and logistic regression to explore the characteristics and perceptions of the first 157 people who agreed to participate in E-TREAT and the predictors of their active engagement in E-TREAT services. In addition, responses to open-ended questions about the participants' experiences with the intervention were analyzed. Results The data reveal that clients who engaged in E-TREAT were more likely than those who did not engage to be female, have children and report a positive relationship with their recovery coach, and were less likely to have completed treatment for a substance use disorder in the past. A majority of people engaging in E-TREAT reported that it was helpful to talk with others with similar problems and that the program assisted them in developing a sense of community. Conclusions The authors conclude that technology-assisted interventions hold promise in expanding access to treatment for substance use disorders especially for women and parents. Further, the characteristics of the relationship with a coach or helper may be critical to engagement in technology-supported interventions
Yoshinaga, Masahiko
2015-01-01
Finite graphs that have a common chromatic polynomial have the same number of regular $n$-colorings. A natural question is whether there exists a natural bijection between regular $n$-colorings. We address this question using a functorial formulation. Let $G$ be a simple graph. Then for each set $X$ we can associate a set of $X$-colorings. This defines a functor, "chromatic functor" from the category of sets with injections to itself. The first main result verifies that two finite graphs dete...
Gross, Jonathan L; Zhang, Ping
2013-01-01
In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition-over 400 pages longer than its predecessor-incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an ex
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
Öçal, Mehmet Fatih
2017-01-01
Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students' learning during graphing functions. However, the display of graphs of functions that students sketched by hand may…
The Interval Graph Completion Problem on Split Graphs
Institute of Scientific and Technical Information of China (English)
ZHANG Zhen-kun; YU Min
2015-01-01
The interval graph completion problem on a graph G is to find an added edge set F such that G+F is an interval supergraph with the smallest possible number of edges. The problem has important applications to numerical algebra, V LSI-layout and algorithm graph theory etc; And it has been known to be N P-complete on general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the interval graph completion problem on split graphs is investigated.
Graph Operations on Clique-Width Bounded Graphs
Gurski, Frank
2007-01-01
Clique-width is a well-known graph parameter. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded clique-width. The same holds for NLC-width. In this paper we study the behavior of clique-width and NLC-width under various graph operations and graph transformations. We give upper and lower bounds for the clique-width and NLC-width of the modified graphs in terms of the clique-width and NLC-width of the involved graphs.
GraphState - a tool for graph identification and labelling
Batkovich, D; Kompaniets, M; Novikov, S
2014-01-01
We present python libraries for Feynman graphs manipulation. The key feature of these libraries is usage of generalization of graph representation offered by B. G. Nickel et al. In this approach graph is represented in some unique 'canonical' form that depends only on its combinatorial type. The uniqueness of graph representation gives an efficient way for isomorphism finding, searching for subgraphs and other graph manipulation tasks. Though offered libraries were originally designed for Feynman graphs, they might be useful for more general graph problems.
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Directory of Open Access Journals (Sweden)
Haynes Teresa W.
2014-08-01
Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds
Categorical constructions in graph theory
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Richard T. Bumby
1986-01-01
Full Text Available This paper presents some graph-theoretic questions from the viewpoint of the portion of category theory which has become common knowledge. In particular, the reader is encouraged to consider whether there is only one natural category of graphs and how theories of directed graphs and undirected graphs are related.
A Semantic Graph Query Language
Energy Technology Data Exchange (ETDEWEB)
Kaplan, I L
2006-10-16
Semantic graphs can be used to organize large amounts of information from a number of sources into one unified structure. A semantic query language provides a foundation for extracting information from the semantic graph. The graph query language described here provides a simple, powerful method for querying semantic graphs.
Local Interaction on Random Graphs
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Hans Haller
2010-08-01
Full Text Available We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph cannot change over time.
The Least Eigenvalue of Graphs
Institute of Scientific and Technical Information of China (English)
Guidong YU; Yizheng FAN; Yi WANG
2012-01-01
In this paper we investigate the least eigenvalue of a graph whose complement is connected,and present a lower bound for the least eigenvalue of such graph.We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.
Solsolitons associated with graphs
Lafuente, Ramiro A
2010-01-01
We show how to associate with each graph with a certain property (positivity) a family of simply connected solvable Lie groups endowed with left-invariant Riemannian metrics that are Ricci solitons (called solsolitons). We classify them up to isometry, obtaining families depending on many parameters of explicit examples of Ricci solitons. A classification of graphs with up to 3 coherent components according to positivity is also given.
Graph Embedding for Pattern Analysis
Ma, Yunqian
2013-01-01
Graph Embedding for Pattern Analysis covers theory methods, computation, and applications widely used in statistics, machine learning, image processing, and computer vision. This book presents the latest advances in graph embedding theories, such as nonlinear manifold graph, linearization method, graph based subspace analysis, L1 graph, hypergraph, undirected graph, and graph in vector spaces. Real-world applications of these theories are spanned broadly in dimensionality reduction, subspace learning, manifold learning, clustering, classification, and feature selection. A selective group of experts contribute to different chapters of this book which provides a comprehensive perspective of this field.
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
Arrighi, Pablo
2016-01-01
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded speed, with respect to the distance given by the graph. Suppose, moreover, that the graph itself is subject to the evolution, and may be driven to be in a quantum superposition of graphs---in accordance to the superposition principle. We show that these unitary causal operators must decompose as a finite-depth circuit of local unitary gates. This unifies a result on Quantum Cellular Automata with another on Reversible Causal Graph Dynamics. Along the way we formalize a notion of causality which is valid in the context of quantum superpositions of time-varying graphs, and has a number of good properties. Keywords: Quantum Lattice Gas Automata, Block-representation, Curtis-Hedlund-Lyndon, No-signalling, Localizability, Quantum Gravity, Quantum Graphity, Causal Dynamical Triangula...
Commuting projections on graphs
Energy Technology Data Exchange (ETDEWEB)
Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zikatanov, Ludmil T. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
2013-02-19
For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ_{2}-projection Q_{H} onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π _{H} from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π _{H} and Q_{H} commute with the discrete divergence operator, i.e., we have div π _{H} = Q_{H} div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.
Clique graphs and overlapping communities
Evans, T. S.
2010-12-01
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of communities or clusters is used to illustrate how a clique graph may be exploited. In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.
Scaffolding: Applications to learning in technology-supported environments.
Collis, Betty; Mcnaughton, Catherine; Oliver, Ron; Winnips, J.C.
1999-01-01
Scaffolding is a form of temporary support offered to a learner to assist in the process of becoming a skilled practitioner. Traditionally, the most common form of learning has been an apprenticeship, where a novice learns through active participation in a task, initially only peripherally, and then
Scaffolding: Applications to learning in technology-supported environments
Collis, Betty; Mcnaughton, Catherine; Oliver, Ron; Winnips, Koos
1999-01-01
Scaffolding is a form of temporary support offered to a learner to assist in the process of becoming a skilled practitioner. Traditionally, the most common form of learning has been an apprenticeship, where a novice learns through active participation in a task, initially only peripherally, and then
Higher-order graph wavelets and sparsity on circulant graphs
Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi
2015-08-01
The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.
Regularity in Vague Intersection Graphs and Vague Line Graphs
Directory of Open Access Journals (Sweden)
Muhammad Akram
2014-01-01
Full Text Available Fuzzy graph theory is commonly used in computer science applications, particularly in database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce the notion of vague line graphs, and certain types of vague line graphs and present some of their properties. We also discuss an example application of vague digraphs.
Technology-Supported Art as a "Way to Participation"
Directory of Open Access Journals (Sweden)
Molly Bathje MS, OTR/L
2014-04-01
Full Text Available Brianna Vitale provided the painting featured on the cover of the Spring 2014 issue of The Open Journal of Occupational Therapy. Brianna completed the painting, titled “Flamingo,” using a mouth joystick (joust to draw the image on her computer and an assistive device to translate her computer artwork into the watercolor painting. At 12 years old, Brianna has been living for the past 9 years with tetraplegia, the result of a spinal cord injury (SCI. Through technology and with the support of family, friends, and health care professionals, Brianna energetically engages in a variety of creative, social, and philanthropic activities.
Scaffold hopping using clique detection applied to reduced graphs.
Barker, Edward J; Buttar, David; Cosgrove, David A; Gardiner, Eleanor J; Kitts, Paula; Willett, Peter; Gillet, Valerie J
2006-01-01
Similarity-based methods for virtual screening are widely used. However, conventional searching using 2D chemical fingerprints or 2D graphs may retrieve only compounds which are structurally very similar to the original target molecule. Of particular current interest then is scaffold hopping, that is, the ability to identify molecules that belong to different chemical series but which could form the same interactions with a receptor. Reduced graphs provide summary representations of chemical structures and, therefore, offer the potential to retrieve compounds that are similar in terms of their gross features rather than at the atom-bond level. Using only a fingerprint representation of such graphs, we have previously shown that actives retrieved were more diverse than those found using Daylight fingerprints. Maximum common substructures give an intuitively reasonable view of the similarity between two molecules. However, their calculation using graph-matching techniques is too time-consuming for use in practical similarity searching in larger data sets. In this work, we exploit the low cardinality of the reduced graph in graph-based similarity searching. We reinterpret the reduced graph as a fully connected graph using the bond-distance information of the original graph. We describe searches, using both the maximum common induced subgraph and maximum common edge subgraph formulations, on the fully connected reduced graphs and compare the results with those obtained using both conventional chemical and reduced graph fingerprints. We show that graph matching using fully connected reduced graphs is an effective retrieval method and that the actives retrieved are likely to be topologically different from those retrieved using conventional 2D methods.
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
Directory of Open Access Journals (Sweden)
Vassilis Giakoumakis
1997-12-01
Full Text Available We study the P 4-tidy graphs, a new class defined by Rusu [30] in order to illustrate the notion of P 4-domination in perfect graphs. This class strictly contains the P 4-extendible graphs and the P 4-lite graphs defined by Jamison & Olariu in [19] and [23] and we show that the P 4-tidy graphs and P 4-lite graphs are closely related. Note that the class of P 4-lite graphs is a class of brittle graphs strictly containing the P 4-sparse graphs defined by Hoang in [14]. McConnel & Spinrad [2] and independently Cournier & Habib [5] have shown that the modular decomposition tree of any graph is computable in linear time. For recognizing in linear time P 4-tidy graphs, we apply a method introduced by Giakoumakis in [9] and Giakoumakis & Fouquet in [6] using modular decomposition of graphs and we propose linear algorithms for optimization problems on such graphs, as clique number, stability number, chromatic number and scattering number. We show that the Hamiltonian Path Problem is linear for this class of graphs. Our study unifies and generalizes previous results of Jamison & Olariu ([18], [21], [22], Hochstattler & Schindler[16], Jung [25] and Hochstattler & Tinhofer [15].
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Dickson, Diane
2015-05-01
Linking theory to practice is an area of concern for ultrasound students, clinical mentors and academic staff. The link between theory and practice requires a robust clinical mentorship scheme in addition to careful curricula design considerations to improve student outcomes. The introduction of interactive technology in education provides ripe opportunity to improve feedback to students to support the link between theory and practice. A series of three interactive learning and teaching activities were designed and delivered to a PostGraduate Ultrasound cohort, after which, evaluation was performed to answer the research question: Which interactive technologies support the link between theory and practice through improved feedback mechanisms? An action research methodology was adopted involving an enquiry based literature review, planning, design and action process. Data were collected following action of three interactive teaching and learning sessions within the Medical Ultrasound cohort of 2013/2014 at Glasgow Caledonian University via a paper based questionnaire. A 100% response rate was achieved (n = 14). All three interactive learning and teaching sessions were considered with 100% highest point agreement to support the link between ultrasound theory and practice via feedback. Students found all three designed and facilitated sessions valuable and relevant to their learning, which in turn provided positive experiences which were perceived to support the link between theory and practice through feedback. These activities can be considered valuable in Postgraduate Ultrasound education.
Optimized Graph Search Using Multi-Level Graph Clustering
Kala, Rahul; Shukla, Anupam; Tiwari, Ritu
Graphs find a variety of use in numerous domains especially because of their capability to model common problems. The social networking graphs that are used for social networking analysis, a feature given by various social networking sites are an example of this. Graphs can also be visualized in the search engines to carry search operations and provide results. Various searching algorithms have been developed for searching in graphs. In this paper we propose that the entire network graph be clustered. The larger graphs are clustered to make smaller graphs. These smaller graphs can again be clustered to further reduce the size of graph. The search is performed on the smallest graph to identify the general path, which may be further build up to actual nodes by working on the individual clusters involved. Since many searches are carried out on the same graph, clustering may be done once and the data may be used for multiple searches over the time. If the graph changes considerably, only then we may re-cluster the graph.
Subdominant pseudoultrametric on graphs
Energy Technology Data Exchange (ETDEWEB)
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Bordenave, Charles; Salez, Justin
2011-01-01
We prove that the local weak convergence of a sequence of graphs is enough to guarantee the convergence of their normalized matching numbers. The limiting quantity is described by a local recursion defined on the weak limit of the graph sequence. However, this recursion may admit several solutions, implying non-trivial long-range dependencies between the edges of a largest matching. We overcome this lack of correlation decay by introducing a perturbative parameter called the temperature, which we let progressively go to zero. When the local weak limit is a unimodular Galton-Watson tree, the recursion simplifies into a distributional equation, resulting into an explicit formula that considerably extends the well-known one by Karp and Sipser for Erd\\"os-R\\'enyi random graphs.
Iacovacci, Jacopo
2015-01-01
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of visibility graph motifs, smaller substructures that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated to general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable to distinguish among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification a...
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Hyperbolicity in Median Graphs
Indian Academy of Sciences (India)
José M Sigarreta
2013-11-01
If is a geodesic metric space and $x_1,x_2,x_3\\in X$, a geodesic triangle $T=\\{x_1,x_2,x_3\\}$ is the union of the three geodesics $[x_1 x_2],[x_2 x_3]$ and $[x_3 x_1]$ in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle in . If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e.,$(X)=\\inf\\{≥ 0: X \\quad\\text{is}\\quad -\\text{hyperbolic}\\}$. In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its bigons are thin.
Erickson, Lindsay
2010-01-01
The game of Nim as played on graphs was introduced in Nim on Graphs I and extended in Nim on Graphs II by Masahiko Fukuyama. His papers detail the calculation of Grundy numbers for graphs under specific circumstances. We extend these results and introduce the strategy for even cycles. This paper examines a more general class of graphs by restricting the edge weight to one. We provide structural conditions for which there exist a winning strategy. This yields the solution for the complete graph.
Graph theory and interconnection networks
Hsu, Lih-Hsing
2008-01-01
The advancement of large scale integrated circuit technology has enabled the construction of complex interconnection networks. Graph theory provides a fundamental tool for designing and analyzing such networks. Graph Theory and Interconnection Networks provides a thorough understanding of these interrelated topics. After a brief introduction to graph terminology, the book presents well-known interconnection networks as examples of graphs, followed by in-depth coverage of Hamiltonian graphs. Different types of problems illustrate the wide range of available methods for solving such problems. The text also explores recent progress on the diagnosability of graphs under various models.
DEFF Research Database (Denmark)
Randerath, Bert; Vestergaard, Preben D.
2010-01-01
A graph G is P3-equipackable if any sequence of successive removals of edge-disjoint copies of P3 from G always terminates with a graph having at most one edge. All P3-equipackable graphs are characterised. They belong to a small number of families listed here.......A graph G is P3-equipackable if any sequence of successive removals of edge-disjoint copies of P3 from G always terminates with a graph having at most one edge. All P3-equipackable graphs are characterised. They belong to a small number of families listed here....
Feynman motives of banana graphs
Aluffi, Paolo
2008-01-01
We consider the infinite family of Feynman graphs known as the ``banana graphs'' and compute explicitly the classes of the corresponding graph hypersurfaces in the Grothendieck ring of varieties as well as their Chern--Schwartz--MacPherson classes, using the classical Cremona transformation and the dual graph, and a blowup formula for characteristic classes. We outline the interesting similarities between these operations and we give formulae for cones obtained by simple operations on graphs. We formulate a positivity conjecture for characteristic classes of graph hypersurfaces and discuss briefly the effect of passing to noncommutative spacetime.
Locally identifying coloring of graphs
Esperet, Louis; Montassier, Mickael; Ochem, Pascal; Parreau, Aline
2010-01-01
A vertex-coloring of a graph G is said to be locally identifying if for any pair (u,v) of adjacent vertices of G, with distinct closed neighborhood, the set of colors that appears in the closed neighborhoods of u and v are distinct. In this paper, we give several bounds on the minimum number of colors needed in such a coloring for different families of graphs (planar graphs, some subclasses of perfect graphs, graphs with bounded maximum degree) and prove that deciding whether a subcubic bipartite graph with large girth has a locally identifying coloring with 3 colors is an NP-complete problem.
Technology support in nursing education: clickers in the classroom.
Berry, Janice
2009-01-01
Research has shown that the present generation of students has a preference for digital literacy, experiential learning, interactivity, and immediacy; therefore, greater use of technology is being brought into university courses to aid in student involvement. Student Response Systems, called clickers, were incorporated as a teaching methodology to enhance student interaction and learning in a didactic pediatric nursing course. This course was taught over Interactive Television (ITV) with students at a distant site as well as face to face, creating the challenge of whole-class engagement. Clickers were used to actively engage students at both sites simultaneously and give immediate feedback to students regarding understanding of lecture material. Clickers also allowed small-group problem solving of questions. Exam grades and level of participation in case studies were monitored and exam scores and final scores were compared to those of a previous class. Student t-tests demonstrated that one of three course exams and final course grades were significantly higher for the students who used clickers in the classroom. Satisfaction feedback also supported the use of clickers as a tool to engage students and enhance learning outcomes.
TECHNOLOGY SUPPORTED LEARNING PLATFORM: Moodle Integrated Academic Course
Directory of Open Access Journals (Sweden)
Saziye YAMAN
2010-04-01
Full Text Available It is substantially accepted that constructivism proposes knowledge as “not a fixed object”; constructed by an individual through her own experiences. As a learning theory, constructivism in education emphasizes collaborative learning, such as authentic challenging projects involving in students, teachers and experts in the learning community. Its goal is to create learning communities that are more closely related to the collaborative practice of the real world as strongly reflected in social constructivist idea. The technologies used in the filed of education will support learning through collaborative practices, using learners’ experiences for “meaning making”. The challenge now is to extend the educational networks so that it offers access to learning resources, online storage and tools for communication and management not just within the limitation of school and time. Through learning platforms, such as Moodle, teachers and administrators may bring hardware, software and supporting services together to enable more effective conditions among teachers and students. In this study, Moodle was used to support the 4th grade pre-service language teachers’ (student teachers one of the academic courses, named as “Field Experience”. The student teachers were expected to prepare graduation theses in the field of English language teaching. Moodle was integrated as a technological learning aid and used as online support throughout a semester course. So, we will discuss how Moodle was integrated as a learning platform, while discussing, the use of Moodle as a “course supporter” process, steps and the sample activities will be presented as well.
Graph-based knowledge representation computational foundations of conceptual graphs
Chein, Michel; Chein, Michel
2008-01-01
In addressing the question of how far it is possible to go in knowledge representation and reasoning through graphs, the authors cover basic conceptual graphs, computational aspects, and kernel extensions. The basic mathematical notions are summarized.
Algorithms for Planar Graphs and Graphs in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
Algorithms for network problems play an increasingly important role in modern society. The graph structure of a network is an abstract and very useful representation that allows classical graph algorithms, such as Dijkstra and Bellman-Ford, to be applied. Real-life networks often have additional...... preprocessing time, an O(n log n) time algorithm for the replacement paths problem, and a min st-cut oracle with nearlinear preprocessing time. We also give improved time bounds for computing various graph invariants such as diameter and girth. In the second part, we consider stretch factor problems...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...
SOME RESULTS ON CIRCULAR PERFECT GRAPHS AND PERFECT GRAPHS
Institute of Scientific and Technical Information of China (English)
XU Baogang
2005-01-01
An r-circular coloring of a graph G is a map f from V(G) to the set of open unit intervals of an Euclidean circle of length r,such that f(u) ∩ f(v) = φ whenever uv ∈ E(G).Circular perfect graphs are defined analogously to perfect graphs by means of two parameters,the circular chromatic number and the circular clique number.In this paper,we study the properties of circular perfect graphs.We give (1) a necessary condition for a graph to be circular perfect,(2) some circular critical imperfect graphs,and (3) a characterization of graphs with the property that each of their induced subgraphs has circular clique number the same as its clique number,and then the two conjectures that are equivalent to the perfect graph conjecture.
Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models
Directory of Open Access Journals (Sweden)
Tomasz Kajdanowicz
2016-09-01
Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.
Institute of Scientific and Technical Information of China (English)
ZHANG Guoqiang; CHEN Yixiang
2001-01-01
This paper provides a concrete and simple introduction to two pillars of domain theory: (1) solving recursive domain equations, and (2) universal and saturated domains. Our exposition combines Larsen and Winskel's idea on solving domain equations using information systems with Girard's idea of stable domain theory in the form of coherence spaces, or graphs.Detailed constructions are given for universal and even homogeneous objects in two categories of graphs: one representing binary complete, prime algebraic domains with complete primes covering the bottom; the other representing ω-algebraic, prime algebraic lattices. The backand-forth argument in model theory helps to enlighten the constructions.
Cheung, King Sing
2014-01-01
Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume
Haynes Teresa W.; Hedetniemi Stephen T.; Jamieson Jessie D.; Jamieson William B.
2014-01-01
A path π = (v1, v2, . . . , vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi) ≥ deg(vi+1), where deg(vi) denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a grap...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Distributed Evolutionary Graph Partitioning
Sanders, Peter
2011-01-01
We present a novel distributed evolutionary algorithm, KaFFPaE, to solve the Graph Partitioning Problem, which makes use of KaFFPa (Karlsruhe Fast Flow Partitioner). The use of our multilevel graph partitioner KaFFPa provides new effective crossover and mutation operators. By combining these with a scalable communication protocol we obtain a system that is able to improve the best known partitioning results for many inputs in a very short amount of time. For example, in Walshaw's well known benchmark tables we are able to improve or recompute 76% of entries for the tables with 1%, 3% and 5% imbalance.
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
AN EFFECTIVE RECOMMENDATIONS BY DIFFUSION ALGORITHM FOR WEB GRAPH MINING
Directory of Open Access Journals (Sweden)
S. Vasukipriya
2013-04-01
Full Text Available The information on the World Wide Web grows in an explosive rate. Societies are relying more on the Web for their miscellaneous needs of information. Recommendation systems are active information filtering systems that attempt to present the information items like movies, music, images, books recommendations, tags recommendations, query suggestions, etc., to the users. Various kinds of data bases are used for the recommendations; fundamentally these data bases can be molded in the form of many types of graphs. Aiming at provided that a general framework on effective DR (Recommendations by Diffusion algorithm for web graphs mining. First introduce a novel graph diffusion model based on heat diffusion. This method can be applied to both undirected graphs and directed graphs. Then it shows how to convert different Web data sources into correct graphs in our models.
Model Selection Framework for Graph-based data
Caceres, Rajmonda S; Schmidt, Matthew C; Miller, Benjamin A; Campbell, William M
2016-01-01
Graphs are powerful abstractions for capturing complex relationships in diverse application settings. An active area of research focuses on theoretical models that define the generative mechanism of a graph. Yet given the complexity and inherent noise in real datasets, it is still very challenging to identify the best model for a given observed graph. We discuss a framework for graph model selection that leverages a long list of graph topological properties and a random forest classifier to learn and classify different graph instances. We fully characterize the discriminative power of our approach as we sweep through the parameter space of two generative models, the Erdos-Renyi and the stochastic block model. We show that our approach gets very close to known theoretical bounds and we provide insight on which topological features play a critical discriminating role.
Kanstrup, Anne Marie; Bertelsen, Pernille; Nohr, Christian
2015-01-01
The aim of this paper is to identify characteristics of patients' contributions to innovation in health information technology (HIT). The paper outlines a theoretical definition of patient innovation and presents an analysis of four digital prototypes and 22 low-fidelity mock-ups designed by people affected by the chronic illness diabetes mellitus. Seventeen families (a total of 60 people) with one or more diabetic family members participated in design activities in a four-year research project focused on the design of digital support for everyday living with diabetes. Our analysis documented the originality of the analysed patient designs and identified three characteristics of patients' designs: socio-technical networks, objects with associated personal meanings and technology supporting the expression of identity. The paper concludes that patient innovation is defined by what is perceived as new by patients and/or others within the social system of adaptation. The analysed patient designs are original (as distinct from replications of or improvements on known products), and their characteristics are innovative contributions to the social system of everyday living with diabetes (i.e. they are perceived as new to the patients in the research study). The results of the analysis contribute to the credentials of patients as key actors in HIT innovation and call for participatory approaches in health informatics.
GraphXML: an XML based graph interchange format
I. Herman (Ivan); M.S. Marshall (Scott)
2000-01-01
textabstractGraphXML is a graph description language in XML that can be used as an interchange format for graph drawing and visualization packages. The generality and rich features of XML make it possible to define an interchange format that not only supports the pure, mathematical description of a
Institute of Scientific and Technical Information of China (English)
Wenjun Xiao
2002-01-01
Wu, Lakshmivarahan and Dhall[5] recently described a deterministic, distributed routing scheme for some special classes of metacyclic graphs. However they have no proof of correctness that the scheme is a shortest path routing algorithm. In the note we give a suboptimal, deterministic routing algorithm.
Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracy
1998-01-01
Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…
Pitts Bannister, Vanessa R.; Jamar, Idorenyin; Mutegi, Jomo W.
2007-01-01
In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…
S.M. Heditniemi (Sandra); R.C. Laskar (R.C.); H.M. Mulder (Martyn)
2012-01-01
textabstractLet $G = (V,E)$ be a graph. A partition $\\pi = \\{V_1, V_2, \\ldots, V_k \\}$ of the vertices $V$ of $G$ into $k$ {\\it color classes} $V_i$, with $1 \\leq i \\leq k$, is called a {\\it quorum coloring} if for every vertex $v \\in V$, at least half of the vertices in the closed neighborhood
Coloring geographical threshold graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
Neural networks and graph theory
Institute of Scientific and Technical Information of China (English)
许进; 保铮
2002-01-01
The relationships between artificial neural networks and graph theory are considered in detail. The applications of artificial neural networks to many difficult problems of graph theory, especially NP-complete problems, and the applications of graph theory to artificial neural networks are discussed. For example graph theory is used to study the pattern classification problem on the discrete type feedforward neural networks, and the stability analysis of feedback artificial neural networks etc.
Temporal Representation in Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Institute of Scientific and Technical Information of China (English)
李浩; 刘群
1989-01-01
Because of the widespread applications of tree and treee graph in computer science,we are interested in studying the reee graph.M.Farber,B.Richter and H.Shang in [1] showed that the graph τ2(G)is 2-edge-connected as |V(G)）≥3，at the same time,we will show the best lower bounds about vertex number and minimum degree of graph τ2(G）.
Energy Technology Data Exchange (ETDEWEB)
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Asteroidal Quadruples in non Rooted Path Graphs
Directory of Open Access Journals (Sweden)
Gutierrez Marisa
2015-11-01
Full Text Available A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed path graphs that are non rooted path graphs. We prove that such graphs always contain an asteroidal quadruple.
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Mining and Indexing Graph Databases
Yuan, Dayu
2013-01-01
Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…
Text analysis for knowledge graphs
Popping, Roel
2007-01-01
The concept of knowledge graphs is introduced as a method to represent the state of the art in a specific scientific discipline. Next the text analysis part in the construction of such graphs is considered. Here the 'translation' from text to graph takes place. The method that is used here is compar
Hopkins, Brian
2004-01-01
The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…
Mining and Indexing Graph Databases
Yuan, Dayu
2013-01-01
Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…
Submanifolds Weakly Associated with Graphs
Indian Academy of Sciences (India)
A Carriazo; L M Fernández; A Rodríguez-Hidalgo
2009-06-01
We establish an interesting link between differential geometry and graph theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low dimensions or belonging to some special families.
Green Globs: A Microcomputer Application for Graphing of Equations.
Dugdale, Sharon
This paper outlines the development of an activity that uses the computer's unique capabilities to provide students with a meaningful and highly motivating experience with the graphing of equations. The basic design of the game calls for the computer to display a coordinate grid on which it graphs any equations that are typed in by the student.…
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Dynamic Representations of Sparse Graphs
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Managing and Mining Graph Data
Aggarwal, Charu C
2010-01-01
Managing and Mining Graph Data is a comprehensive survey book in graph management and mining. It contains extensive surveys on a variety of important graph topics such as graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies a number of domain-specific scenarios such as stream mining, web graphs, social networks, chemical and biological data. The chapters are written by well known researchers in the field, and provide a broad perspective of the area. This is the first comprehensive survey book in t
Spectral fluctuations of quantum graphs
Energy Technology Data Exchange (ETDEWEB)
Pluhař, Z. [Faculty of Mathematics and Physics, Charles University, 180 00 Praha 8 (Czech Republic); Weidenmüller, H. A. [Max-Planck-Institut für Kernphysik, 69029 Heidelberg (Germany)
2014-10-15
We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry.
Boxicity of Circular Arc Graphs
Bhowmick, Diptendu; Chandran, L. Sunil
2008-01-01
A $k$-dimensional box is the cartesian product $R_1 \\times R_2 \\times ... \\times R_k$ where each $R_i$ is a closed interval on the real line. The {\\it boxicity} of a graph $G$, denoted as $box(G)$, is the minimum integer $k$ such that $G$ can be represented as the intersection graph of a collection of $k$-dimensional boxes: that is two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a graph that can be represented as the intersection graph of ...
Towards Scalable Graph Computation on Mobile Devices.
Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng
2014-10-01
Mobile devices have become increasingly central to our everyday activities, due to their portability, multi-touch capabilities, and ever-improving computational power. Such attractive features have spurred research interest in leveraging mobile devices for computation. We explore a novel approach that aims to use a single mobile device to perform scalable graph computation on large graphs that do not fit in the device's limited main memory, opening up the possibility of performing on-device analysis of large datasets, without relying on the cloud. Based on the familiar memory mapping capability provided by today's mobile operating systems, our approach to scale up computation is powerful and intentionally kept simple to maximize its applicability across the iOS and Android platforms. Our experiments demonstrate that an iPad mini can perform fast computation on large real graphs with as many as 272 million edges (Google+ social graph), at a speed that is only a few times slower than a 13″ Macbook Pro. Through creating a real world iOS app with this technique, we demonstrate the strong potential application for scalable graph computation on a single mobile device using our approach.
Resolvability in Circulant Graphs
Institute of Scientific and Technical Information of China (English)
Muhammad SALMAN; Imran JAVAID; Muhammad Anwar CHAUDHRY
2012-01-01
A set W of the vertices of a connected graph G is called a resolving set for G if for every two distinct vertices u,v ∈ V(G) there is a vertex w ∈ W such that d(u,w) ≠ d(v,w).A resolving set of minimum cardinality is called a metric basis for G and the number of vertices in a metric basis is called the metric dimension of G,denoted by dim(G).For a vertex u of G and a subset S of V(G),the distance between u and S is the number mins∈s d(u,s).A k-partition H ={S1,S2,...,Sk} of V(G) is called a resolving partition if for every two distinct vertices u,v ∈ V(G) there is a set Si in Π such that d(u,Si) ≠ d(v,Si).The minimum k for which there is a resolving k-partition of V(G) is called the partition dimension of G,denoted by pd(G).The circulant graph is a graph with vertex set Zn,an additive group ofintegers modulo n,and two vertices labeled i and j adjacent if and only if i - j (mod n) ∈ C,where C C Zn has the property that C =-C and 0(∈) C.The circulant graph is denoted by Xn,△ where A =|C|.In this paper,we study the metric dimension of a family of circulant graphs Xn,3 with connection set C ={1,-n/2,n - 1} and prove that dim(Xn,3) is independent of choice of n by showing that 3 for all n =0 (mod 4),dim(X,n,3) ={ 4 for all n =2 (mod 4).We also study the partition dimension of a family of circulant graphs Xn,4 with connection set C ={±1,±2} and prove that pd(Xn,4) is independent of choice of n and show that pd(X5,4) =5 and 3 forall odd n≥9,pd(Xn,4) ={ 4 for all even n ≥ 6 and n =7.
Conditional coloring of some parameterized graphs
Reddy, P Venkata Subba
2010-01-01
For integers k>0 and r>0, a conditional (k,r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex v of degree d(v) in G is adjacent to vertices with at least min{r,d(v)} different colors. The smallest integer k for which a graph G has a conditional (k,r)-coloring is called the rth order conditional chromatic number, denoted by $\\chi_r(G)$. For different values of r we obtain $\\chi_r(G)$ of certain parameterized graphs viz., Windmill graph, line graph of Windmill graph, middle graph of Friendship graph, middle graph of a cycle, line graph of Friendship graph, middle graph of complete k-partite graph and middle graph of a bipartite graph.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Hierarchy of Modular Graph Identities
D'Hoker, Eric
2016-01-01
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analy...
Valiant Transform of Forney Graphs
Al-Bashabsheh, Ali
2010-01-01
The introduction of Forney graphs, or normal graphs, and the duality result therein [1] is a landmark in the theory of codes on graphs and in graph-based iterative decoding. A generic modeling framework for codes and systems, Forney graphs have since found various applications. It is unfortunate however that the development of the theory and application of Forney graphs to date has been restricted to the context of linear (and group) codes and systems, and the primary tool of Forney graphs is the duality result introduced in [1]. In a rather distant area of computer science, Valiant has recently presented a powerful family of new algorithms, which he calls holographic algorithms [2]. Using holographic algorithms, Valiant provides polynomial-time solutions to families of problems previously unknown to be tractable. At the heart of Valiant's holographic algorithms is the notion of "holographic reduction", which is the engine used in holographic algorithms to reduce from one problem to another. Recognizing the c...
Bond percolation on isoradial graphs
Grimmett, Geoffrey
2012-01-01
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star-triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the sense that the one-arm and 2j-alternating-arm critical exponents (and therefore also the connectivity and volume exponents) are constant across the family of such percolation processes. The isoradial graphs in question are those that satisfy certain weak conditions on their embedding and on their track system. This class of graphs includes, for example, isoradial embeddings of periodic graphs, and graphs derived from rhombic Penrose tilings.
Jordan, Jonathan
2011-01-01
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random element, and there are three parameters, $\\alpha$, $\\beta$ and $\\gamma$, which are the probabilities of edges appearing between different types of vertices. We show that as the probabilities associated with the model vary there are a number of phase transitions, in particular concerning the degree sequence. If $(1+\\alpha)(1+\\gamma)1$ then the degree of a typical vertex grows to infinity, and the proportion of vertices having any fixed degree $d$ tends to zero. We also give some results on the number of edges and on the spectral gap.
Normal Order: Combinatorial Graphs
Solomon, A I; Blasiak, P; Horzela, A; Penson, K A; Solomon, Allan I.; Duchamp, Gerard; Blasiak, Pawel; Horzela, Andrzej; Penson, Karol A.
2004-01-01
A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators. In the general case, upon which we touch briefly, this problem leads to combinatorial numbers, the so-called Rook numbers. Since we assume that the two species, bosons and fermions, commute, we subsequently restrict ourselves to consideration of a single species, single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, specifically Bell and Stirling numbers. We explicitly give the generating functions for some classes of these numbers. In this note we concentrate on the combinatorial graph approach, showing how some important classical results of graph theory lead to transparent representations of the combinatorial numbers associated with the boson normal ordering problem.
Exponential random graph models
Fronczak, Agata
2012-01-01
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power. An excellent basic discussion of exponential random graphs addressed to social science students and researchers is given in [Anderson et al., 1999][Robins et al., 2007]. This essay is intentionally designed to be more theoretical in comparison with the well-known primers just mentioned. Given the interdisciplinary character of the new emerging science of complex networks, the essay aims to give a contribution upon which network scientists and practitioners, who represent different research areas, could build a common area of understanding.
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Zhou, Feng; de la Torre, Fernando
2015-11-19
Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.
Lorscheid, Oliver
2010-01-01
Let $X$ be a curve over $\\F_q$ with function field $F$. In this paper, we define a graph for each Hecke operator with fixed ramification. A priori, these graphs can be seen as a convenient language to organize formulas for the action of Hecke operators on automorphic forms. However, they will prove to be a powerful tool for explicit calculations and proofs of finite dimensionality results. We develop a structure theory for certain graphs $G_x$ of unramified Hecke operators, which is of a similar vein to Serre's theory of quotients of Bruhat Tits trees. To be precise, $G_x$ is locally a quotient of a Bruhat Tits tree and has finitely many components. An interpretation of $G_x$ in terms of rank 2 bundles on $X$ and methods from reduction theory show that $G_x$ is the union of finitely many cusps, which are infinite subgraphs of a simple nature, and a nucleus, which is a finite subgraph that depends heavily on the arithmetics of $F$. We describe how one recovers unramified automorphic forms as functions on the g...
Kinetic Stable Delaunay Graphs
Agarwal, Pankaj K; Guibas, Leonidas J; Kaplan, Haim; Koltun, Vladlen; Rubin, Natan; Sharir, Micha
2011-01-01
We consider the problem of maintaining the Euclidean Delaunay triangulation $\\DT$ of a set $P$ of $n$ moving points in the plane, along algebraic trajectories of constant description complexity. Since the best known upper bound on the number of topological changes in the full $\\DT$ is nearly cubic, we seek to maintain a suitable portion of it that is less volatile yet retains many useful properties. We introduce the notion of a stable Delaunay graph, which is a dynamic subgraph of the Delaunay triangulation. The stable Delaunay graph (a) is easy to define, (b) experiences only a nearly quadratic number of discrete changes, (c) is robust under small changes of the norm, and (d) possesses certain useful properties. The stable Delaunay graph ($\\SDG$ in short) is defined in terms of a parameter $\\alpha>0$, and consists of Delaunay edges $pq$ for which the angles at which $p$ and $q$ see their Voronoi edge $e_{pq}$ are at least $\\alpha$. We show that (i) $\\SDG$ always contains at least roughly one third of the Del...
The phylogeny graphs of doubly partial orders
Park, Boram
2011-01-01
The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced subgraph, respectively. Phylogeny graphs are variant of competition graphs. The phylogeny graph $P(D)$ of a digraph $D$ is the (simple undirected) graph defined by $V(P(D)):=V(D)$ and $E(P(D)):=\\{xy \\mid N^+_D(x) \\cap N^+_D(y) \
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-01
This final technical report was prepared by Rolls-Royce Allison summarizing the multiyear activities of the Advanced Turbine Technology Applications Project (ATTAP) and the Hybrid Vehicle Turbine Engine Technology Support (HVTE-TS) project. The ATTAP program was initiated in October 1987 and continued through 1993 under sponsorship of the US Department of Energy (DOE), Energy Conservation and Renewable Energy, Office of Transportation Technologies, Propulsion Systems, Advanced Propulsion Division. ATTAP was intended to advance the technological readiness of the automotive ceramic gas turbine engine. The target application was the prime power unit coupled to conventional transmissions and powertrains. During the early 1990s, hybrid electric powered automotive propulsion systems became the focus of development and demonstration efforts by the US auto industry and the Department of energy. Thus in 1994, the original ATTAP technology focus was redirected to meet the needs of advanced gas turbine electric generator sets. As a result, the program was restructured to provide the required hybrid vehicle turbine engine technology support and the project renamed HVTE-TS. The overall objective of the combined ATTAP and HVTE-TS projects was to develop and demonstrate structural ceramic components that have the potential for competitive automotive engine life cycle cost and for operating 3,500 hr in an advanced high temperature turbine engine environment. This report describes materials characterization and ceramic component development, ceramic components, hot gasifier rig testing, test-bed engine testing, combustion development, insulation development, and regenerator system development. 130 figs., 12 tabs.
Duality in Geometric Graphs: Vector Graphs, Kirchhoff Graphs and Maxwell Reciprocal Figures
Directory of Open Access Journals (Sweden)
Tyler Reese
2016-02-01
Full Text Available We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the intuitive notion of drawing graphs with edges taken as vectors. This leads to a discussion of Kirchhoff graphs, as originally presented by Fehribach, which can be defined independent of any matrix relations. In particular, we present simple cases in which vector graphs are guaranteed to be Kirchhoff or non-Kirchhoff. Next, we review Maxwell’s method of drawing reciprocal figures as he presented in 1864, using modern mathematical language. We then demonstrate cases in which R2-vector graphs defined from Maxwell reciprocals are “dual” Kirchhoff graphs. Given an example in which Maxwell’s theories are not sufficient to define vector graphs, we begin to explore other methods of developing dual Kirchhoff graphs.
Technology-Supported Peer Feedback in ESL/EFL Writing Classes: A Research Synthesis
Chen, Tsuiping
2016-01-01
Some studies on technology-supported peer feedback in the writing classroom claim that it reduces the threatening atmosphere caused by face-to-face interaction and that the discourse patterns and language use in the electronic feedback are more flexible than in spoken discourse. Others present a negative view that the comments generated from…
Anderson, Lori S.; Enge, Karmin J.
2012-01-01
School nurses care for children with a variety of health-related conditions and they need information about managing these conditions, which is accessible, current, and useful. The goal of this literature review was to gather and synthesize information on technology-supported resources and to determine which met the educational needs of school…
Healthcare professional behaviour change using technological supports: A realist literature review
Directory of Open Access Journals (Sweden)
Chris Keyworth
2015-10-01
Technological supports aiming to change the behaviour of healthcare professionals show considerable promise, particularly those involving computer-generated reminders and feedback. Due to the lack of theoretically-informed interventions, we were unable to draw conclusions around the effectiveness of theory-behaviour change interventions in this context. Interventions currently lack consistency in delivery method and content, which future research should address.
Ben-Moussa, M.; Rubo, M.; Debracque, C.; Lange, W.G.
2017-01-01
The present paper explores the benefits and the capabilities of various emerging state-of-the-art interactive 3D and Internet of Things (IoT) technologies and investigates how these technologies can be exploited to develop a more effective technology supported exposure therapy solution for Social
Self-Assessment in a Technology-Supported Environment: The Case of Grade 9 Geography
Ross, John A.; Starling, Michelle
2008-01-01
We investigated the impact of self-assessment training on student achievement and on computer self-efficacy in a technology-supported learning environment (grade 9 students using Global Information Systems software). We found that self-assessment had a positive effect on student achievement, accounting for 25% of the variance across three…
Proceedings of the 1st Workshop on Technology Support for Self-Organized Learners
Kalz, Marco; Koper, Rob; Hornung-Prähauser, Veronika; Luckmann, Michaela
2008-01-01
Kalz, M., Koper, R., Hornung-Prähauser, V., & Luckmann, M. (Eds.) (2008). Proceedings of the 1st Workshop on Technology Support for Self-Organized Learners. June, 2-3, 2008, Salzburg, Austria: CEUR Workshop Proceedings, ISSN 1613-0073. Available at http://ceur-ws.org/Vol-349.
Graphs cospectral with a friendship graph or its complement
Directory of Open Access Journals (Sweden)
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
Evaluation of Graph Pattern Matching Workloads in Graph Analysis Systems
Energy Technology Data Exchange (ETDEWEB)
Hong, Seokyong [North Carolina State University (NCSU), Raleigh; Lee, Sangkeun (Matt) [ORNL; Lim, Seung-Hwan [ORNL; Sukumar, Sreenivas Rangan [ORNL; Vatsavai, Raju [North Carolina State University (NCSU), Raleigh
2016-01-01
Graph analysis has emerged as a powerful method for data scientists to represent, integrate, query, and explore heterogeneous data sources. As a result, graph data management and mining became a popular area of research, and led to the development of plethora of systems in recent years. Unfortunately, the number of emerging graph analysis systems and the wide range of applications, coupled with a lack of apples-to-apples comparisons, make it difficult to understand the trade-offs between different systems and the graph operations for which they are designed. A fair comparison of these systems is a challenging task for the following reasons: multiple data models, non-standardized serialization formats, various query interfaces to users, and diverse environments they operate in. To address these key challenges, in this paper we present a new benchmark suite by extending the Lehigh University Benchmark (LUBM) to cover the most common capabilities of various graph analysis systems. We provide the design process of the benchmark, which generalizes the workflow for data scientists to conduct the desired graph analysis on different graph analysis systems. Equipped with this extended benchmark suite, we present performance comparison for nine subgraph pattern retrieval operations over six graph analysis systems, namely NetworkX, Neo4j, Jena, Titan, GraphX, and uRiKA. Through the proposed benchmark suite, this study reveals both quantitative and qualitative findings in (1) implications in loading data into each system; (2) challenges in describing graph patterns for each query interface; and (3) different sensitivity of each system to query selectivity. We envision that this study will pave the road for: (i) data scientists to select the suitable graph analysis systems, and (ii) data management system designers to advance graph analysis systems.
An Algebraic Representation of Graphs and Applications to Graph Enumeration
Directory of Open Access Journals (Sweden)
Ângela Mestre
2013-01-01
Full Text Available We give a recursion formula to generate all the equivalence classes of connected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We use an algebraic graph representation to apply the result to the enumeration of connected graphs, all of whose biconnected components have the same number of vertices and edges. The proof uses Abel’s binomial theorem and generalizes Dziobek’s induction proof of Cayley’s formula.
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
DEFF Research Database (Denmark)
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...
Spectral Radius of Hamiltonian Planar Graphs and Outerplanar Graphs
Institute of Scientific and Technical Information of China (English)
周建; 林翠琴; 胡冠章
2001-01-01
The spectral radius is an important parameter of a graph related to networks. A method forestimating the spectral radius of each spanning subgraph is used to prove that the spectral radius of aHamiltonian planar graph of order n ≥ 4 is less than or equal toand the spectral radius of theouterplanar graph of order n ≥ 6 is less than or equal to, which are improvements overprevious results. A direction for further study is then suggested.``
Studying the corona product of graphs under some graph invariants
Directory of Open Access Journals (Sweden)
M. Tavakoli
2014-09-01
Full Text Available The corona product $Gcirc H$ of two graphs $G$ and $H$ is obtained by taking one copy of $G$ and $|V(G|$ copies of $H$; and by joining each vertex of the $i$-th copy of $H$ to the $i$-th vertex of $G$, where $1 leq i leq |V(G|$. In this paper, exact formulas for the eccentric distance sum and the edge revised Szeged indices of the corona product of graphs are presented. We also study the conditions under which the corona product of graphs produces a median graph.
Graph Coarsening for Path Finding in Cybersecurity Graphs
Energy Technology Data Exchange (ETDEWEB)
Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh
2013-01-01
n the pass-the-hash attack, hackers repeatedly steal password hashes and move through a computer network with the goal of reaching a computer with high level administrative privileges. In this paper we apply graph coarsening in network graphs for the purpose of detecting hackers using this attack or assessing the risk level of the network's current state. We repeatedly take graph minors, which preserve the existence of paths in the graph, and take powers of the adjacency matrix to count the paths. This allows us to detect the existence of paths as well as find paths that have high risk of being used by adversaries.
Statistical mechanics on isoradial graphs
Boutillier, Cédric
2010-01-01
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs naturally arise in two approaches used by physicists: transfer matrices and conformal field theory. This leads us to the fact that isoradial graphs provide a natural setting for discrete complex analysis, to which we dedicate one section. Then, we give an overview of explicit results obtained for different models of statistical mechanics defined on such graphs: the critical dimer model when the underlying graph is bipartite, the 2-dimensional critical Ising model, random walk and spanning trees and the q-state Potts model.
Eilers, Søren; Sørensen, Adam P W
2011-01-01
We provide a complete invariant for graph C*-algebras which are amplified in the sense that whenever there is an edge between two vertices, there are infinitely many. The invariant used is the standard primitive ideal space adorned with a map into {-1,0,1,2,...}, and we prove that the classification result is strong in the sense that isomorphisms at the level of the invariant always lift. We extend the classification result to cover more graphs, and give a range result for the invariant (in the vein of Effros-Handelman-Shen) which is further used to prove that extensions of graph C*-algebras associated to amplified graphs are again graph C*-algebras of amplified graphs.
Dettlaff, Magda; Yero, Ismael G
2012-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some Cartesian product, strong product or direct product of two paths.
Dettlaff, Magda; Lemanska, Magdalena; Yero, Ismael G.
2012-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
Graphs Theory and Applications
Fournier, Jean-Claude
2008-01-01
This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the
Burleigh, Scott C.
2011-01-01
Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic
DEFF Research Database (Denmark)
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
Motivation RNA folding is a complicated kinetic process. The minimum free energy structure provides only a static view of the most stable conformational state of the system. It is insufficient to give detailed insights into the dynamic behavior of RNAs. A sufficiently sophisticated analysis...... of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
Zeps, Dainis
2009-01-01
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces. Further, we define multiplication of these objects, that coincides with the multiplication of permutations. We consider closed under multiplication classes of combinatorial maps that consist of closed classes of combinatorial maps with fixed edges where each such class is defined by a knot. One class among them is special, containing selfconjugate maps.
Learning Probabilistic Decision Graphs
DEFF Research Database (Denmark)
Jaeger, Manfred; Dalgaard, Jens; Silander, Tomi
2004-01-01
Probabilistic decision graphs (PDGs) are a representation language for probability distributions based on binary decision diagrams. PDGs can encode (context-specific) independence relations that cannot be captured in a Bayesian network structure, and can sometimes provide computationally more...... efficient representations than Bayesian networks. In this paper we present an algorithm for learning PDGs from data. First experiments show that the algorithm is capable of learning optimal PDG representations in some cases, and that the computational efficiency of PDG models learned from real-life data...
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Partitions of generalized split graphs
Shklarsky, Oren
2012-01-01
We discuss matrix partition problems for graphs that admit a partition into k independent sets and ` cliques. We show that when k + ` 6 2, any matrix M has finitely many (k; `) minimal obstructions and hence all of these problems are polynomial time solvable. We provide upper bounds for the size of any (k; `) minimal obstruction when k = ` = 1 (split graphs), when k = 2; ` = 0 (bipartite graphs), and when k = 0; ` = 2 (co-bipartite graphs). When k = ` = 1, we construct an exponential size spl...
Nested Dynamic Condition Response Graphs
DEFF Research Database (Denmark)
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...... Exformatics, a danish provider of case and workflow management systems. We formalize the semantics by giving first a map from Nested to (flat) DCR Graphs with milestones, and then extending the previously given mapping from DCR Graphs to Buchi-automata to include the milestone relation....
Edge Ideals of Weighted Graphs
Paulsen, Chelsey
2012-01-01
We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the combinatorics of "weighted vertex covers". We use these, for instance, to say when these ideals are m-unmixed. We explicitly describe which weighted cycles and trees are unmixed and which ones are Cohen-Macaulay, and we prove that all weighted complete graphs are Cohen-Macaulay.
Intuitionistic Fuzzy Graphs with Categorical Properties
Directory of Open Access Journals (Sweden)
Hossein Rashmanlou
2015-09-01
Full Text Available The main purpose of this paper is to show the rationality of some operations, defined or to be defined, on intuitionistic fuzzy graphs. Firstly, three kinds of new product operations (called direct product, lexicographic product, and strong product are defined in intuitionistic fuzzy graphs, and some important notions on intuitionistic fuzzy graphs are demonstrated by characterizing these notions and their level counterparts graphs such as intuitionistic fuzzy complete graph, cartesian product of intuitionistic fuzzy graphs, composition of intuitionistic fuzzy graphs, union of intuitionistic fuzzy graphs, and join of intuitionistic fuzzy graphs. As a result, a kind of representations of intuitionistic fuzzy graphs and intuitionistic fuzzy complete graphs are given. Next, categorical goodness of intuitionistic fuzzy graphs is illustrated by proving that the category of intuitionistic fuzzy graphs and homomorphisms between them is isomorphic-closed, complete, and co-complete.
Bootstrap Percolation on Random Geometric Graphs
Bradonjić, Milan
2012-01-01
Bootstrap percolation has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of collective action and cultural fads in human societies. It is defined on an (arbitrary) network of interacting agents whose state is determined by the state of their neighbors according to a threshold rule. In a typical setting, bootstrap percolation starts by random and independent "activation" of nodes with a fixed probability $p$, followed by a deterministic process for additional activations based on the density of active nodes in each neighborhood ($\\th$ activated nodes). Here, we study bootstrap percolation on random geometric graphs in the regime when the latter are (almost surely) connected. Random geometric graphs provide an appropriate model in settings where the neighborhood structure of each node is determined by geographical distance, as in wireless {\\it ad hoc} ...
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
On Bipolar Single Valued Neutrosophic Graphs
SAID BROUMI; MOHAMED TALEA; ASSIA BAKALI; FLORENTIN SMARANDACHE
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Double-Critical Graphs and Complete Minors
DEFF Research Database (Denmark)
Kawarabayashi, Ken-ichi; Pedersen, Anders Sune; Toft, Bjarne
2010-01-01
A connected $k$-chromatic graph $G$ is double-critical if for all edges $uv$ of $G$ the graph $G - u - v$ is $(k-2)$-colourable. The only known double-critical $k$-chromatic graph is the complete $k$-graph $K_k$. The conjecture that there are no other double-critical graphs is a special case...
Tutte Polynomial of Multi-Bridge Graphs
Directory of Open Access Journals (Sweden)
Julian A. Allagan
2013-10-01
Full Text Available In this paper, using a well-known recursion for computing the Tutte polynomial of any graph, we found explicit formulae for the Tutte polynomials of any multi-bridge graph and some $2-$tree graphs. Further, several recursive formulae for other graphs such as the fan and the wheel graphs are also discussed.
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, A.; Ehrig, H.; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract graphs
Wang, Suijie
2010-01-01
In this paper, we give a Laplacian characterization of the product of the complete graphs $K_m$ with trees, unicyclic graphs, and bicyclic graphs. More precisely, let $G$ be a connected graph with at most two independent cycles. If $G$ is neither $C_{6}$ nor $\\Theta_{3,2,5}$ and determined by its Laplacain spectrum, then the product $G\\times K_{m}$ is also a graph determined by its Laplacian spectrum. In addition, we find the cosepctral graphs of $C_{6}\\times K_{m}$ and $\\Theta_{3,2,5}\\times K_{m}$, where the case $m=1$ is shown in Figure \\ref{F1} and \\ref{F2}.
A graph theoretical analysis of certain aspects of Bahasa Indonesia
Hoede, C.; Nurdiati, S.
2008-01-01
In this paper the theory of knowledge graphs is applied to some characteristic features of the Indonesian language. The characteristic features to be considered are active and passive form of verbs and the derived nouns
Detecting alternative graph clusterings.
Mandala, Supreet; Kumara, Soundar; Yao, Tao
2012-07-01
The problem of graph clustering or community detection has enjoyed a lot of attention in complex networks literature. A quality function, modularity, quantifies the strength of clustering and on maximization yields sensible partitions. However, in most real world networks, there are an exponentially large number of near-optimal partitions with some being very different from each other. Therefore, picking an optimal clustering among the alternatives does not provide complete information about network topology. To tackle this problem, we propose a graph perturbation scheme which can be used to identify an ensemble of near-optimal and diverse clusterings. We establish analytical properties of modularity function under the perturbation which ensures diversity. Our approach is algorithm independent and therefore can leverage any of the existing modularity maximizing algorithms. We numerically show that our methodology can systematically identify very different partitions on several existing data sets. The knowledge of diverse partitions sheds more light into the topological organization and helps gain a more complete understanding of the underlying complex network.
Estrada, Ernesto
2015-01-01
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square \\left[0,1\\right]^{2}. The topological properties, such as connectivity, average degree, average path length and clustering, of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b=1/a, and the radius r used to connect the nodes. When a=1 we recover the RGG, and when a\\rightarrow\\infty the very elongated rectangle generated resembles a one-dimensional RGG. We provided computational and analytical evidence that the topological properties of the RRG differ significantly from those of the RGG. The connectivity of the RRG depends not only on the number of nodes as in the case of the RGG, but also on the side length of the rectangle. As the rectangle is more elongated the critical radius for connectivity increases following first a power-law an...
Energy Technology Data Exchange (ETDEWEB)
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Kirkpatrick, Bonnie; Reshef, Yakir; Finucane, Hilary; Jiang, Haitao; Zhu, Binhai; Karp, Richard M
2012-09-01
Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic data from a set of extant individuals and reconstruct ancestral individuals. There is a great need to evaluate the quality of these methods by comparing the estimated pedigree to the true pedigree. In this article, we consider two main pedigree comparison problems. The first is the pedigree isomorphism problem, for which we present a linear-time algorithm for leaf-labeled pedigrees. The second is the pedigree edit distance problem, for which we present (1) several algorithms that are fast and exact in various special cases, and (2) a general, randomized heuristic algorithm. In the negative direction, we first prove that the pedigree isomorphism problem is as hard as the general graph isomorphism problem, and that the sub-pedigree isomorphism problem is NP-hard. We then show that the pedigree edit distance problem is APX-hard in general and NP-hard on leaf-labeled pedigrees. We use simulated pedigrees to compare our edit-distance algorithms to each other as well as to a branch-and-bound algorithm that always finds an optimal solution.
Quantization of gauge fields, graph polynomials and graph homology
Energy Technology Data Exchange (ETDEWEB)
Kreimer, Dirk, E-mail: kreimer@physik.hu-berlin.de [Humboldt University, 10099 Berlin (Germany); Sars, Matthias [Humboldt University, 10099 Berlin (Germany); Suijlekom, Walter D. van [Radboud University Nijmegen, 6525 AJ Nijmegen (Netherlands)
2013-09-15
We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.
2005-06-01
intuitive results on a variety of synthetic and real-world datasets. Here, we will verify their scalability. Figure 5.9 shows results on a “ caveman ...show timing results on a “ caveman ” graph with 3 caves. The plot shows wall-clock time vs. the number of edges E in the graph, for both SPLIT (dashed
Subgraph Enumeration in Massive Graphs
DEFF Research Database (Denmark)
Silvestri, Francesco
bound also applies with high probability. Our algorithm is I/O optimal, in the worst-case, when the sample graph belongs to the Alon class, which includes cliques, cycles and every graph with a perfect matching: indeed, we show that any algorithm enumerating $T$ instances must always use $\\BOM...
Open Graphs and Monoidal Theories
Dixon, Lucas
2010-01-01
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to vertices at both ends, and these unconnected ends can be interpreted as the inputs and outputs of a diagram. In this paper, we give a concrete construction for string diagrams using a special kind of typed graph called an open-graph. While the category of open-graphs is not itself adhesive, we introduce the notion of a selective adhesive functor, and show that such a functor embeds the category of open-graphs into the ambient adhesive category of typed graphs. Using this functor, the category of open-graphs inherits "enough adhesivity" from the category of typed graphs to perform double-pushout (DPO) graph rewriting. A salient feature of our theory is that it ensures rewrite systems are "type-safe" in the sense that rewriting respects the inputs and outputs. This formalism lets u...
Network reconstruction via graph blending
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
Graph Transformation and AI Planning
Edelkamp, S.; Rensink, Arend; Edelkamp, S.; Frank, J.
This document provides insight to the similarities and differences of Graph Transformation and AI Planning, two rising research fields with different publication organs and tools. While graph transformation systems can be used as a graphical knowledge engineering front-end for designing planning
Graph Transformation and AI Planning
Edelkamp, S.; Rensink, A.; Edelkamp, S.; Frank, J.
2007-01-01
This document provides insight to the similarities and differences of Graph Transformation and AI Planning, two rising research fields with different publication organs and tools. While graph transformation systems can be used as a graphical knowledge engineering front-end for designing planning pr
Quantum Markov fields on graphs
2009-01-01
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we construct the entangled Markov fields on tree graphs. The concrete examples of generalized d-Markov chains on Cayley trees are also investigated.
Paley Graphs and Their Generalizations
Elsawy, Ahmed Noubi
2012-01-01
To construct a Paley graph, we fix a finite field and consider its elements as vertices of the Paley graph. Two vertices are connected by an edge if their difference is a square in the field. We will study some important properties of the Paley graphs. In particular, we will show that the Paley graphs are connected, symmetric, and self-complementary. Also we will show that the Paley graph of order q is (q-1)/2 -regular, and every two adjacent vertices have (q-5)/4 common neighbors, and every two non-adjacent vertices have q-1/4 common neighbors, which means that the Paley graphs are strongly regular with parameters(q,q-1/2,q-5/4, q-1/4). Paley graphs are generalized by many mathematicians. In the first section of Chapter 3 we will see three examples of these generalizations and some of their basic properties. In the second section of Chapter 3 we will define a new generalization of the Paley graphs, in which pairs of elements of a finite field are connected by an edge if and only if there difference belongs t...
Graph Representation of Projective Resolutions
Institute of Scientific and Technical Information of China (English)
Hong Bo SHI
2011-01-01
We generalize the concept - dimension tree and the related results for monomial algebras to a more general case - relations algebras Λ by bringing Gr(o)bner basis into play. More precisely,graph to be called the minimal resolution graph for M. Algorithms for computing such diagraphs and applications as well will be presented.
A Collection of Features for Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Eliassi-Rad, T; Fodor, I K; Gallagher, B
2007-05-02
Semantic graphs are commonly used to represent data from one or more data sources. Such graphs extend traditional graphs by imposing types on both nodes and links. This type information defines permissible links among specified nodes and can be represented as a graph commonly referred to as an ontology or schema graph. Figure 1 depicts an ontology graph for data from National Association of Securities Dealers. Each node type and link type may also have a list of attributes. To capture the increased complexity of semantic graphs, concepts derived for standard graphs have to be extended. This document explains briefly features commonly used to characterize graphs, and their extensions to semantic graphs. This document is divided into two sections. Section 2 contains the feature descriptions for static graphs. Section 3 extends the features for semantic graphs that vary over time.
Asymptotic aspects of Cayley graphs
Dejter, Italo J
2011-01-01
Arising from complete Cayley graphs $\\Gamma_n$ of odd cyclic groups $\\Z_n$, an asymptotic approach is presented on connected labeled graphs whose vertices are labeled via equally-multicolored copies of $K_4$ in $\\Gamma_n$ with adjacency of any two such vertices whenever they are represented by copies of $K_4$ in $\\Gamma_n$ sharing two equally-multicolored triangles. In fact, these connected labeled graphs are shown to form a family of graphs of largest degree 6 and diameter asymptotically of order $|V|^{1/3}$, properties shared by the initial member of a collection of families of Cayley graphs of degree $2m\\geq 6$ with diameter asymptotically of order $|V|^{1/m}$, where $3\\leq m\\in\\Z$.
Renormalization algorithm with graph enhancement
Hübener, R; Hartmann, L; Dür, W; Plenio, M B; Eisert, J
2011-01-01
We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)] to other tensor-network states such as the tensor tree states (TTS) and projected entangled pair states (PEPS). We investigate the suitability of the bare TTS to describe ground states, showing that the description of certain graph states and condensed matter models improves. We investigate graph-enhanced tensor-network states, demonstrating that in some cases (disturbed graph states and for certain quantum circuits) the combination of weighted graph states with tensor tree states can greatly improve the accuracy of the description of ground states and time evolved states. We comment on delineating the boundary of the classically efficiently simulatable states of quantum many-body systems.
Planar graphs theory and algorithms
Nishizeki, T
1988-01-01
Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.
Quantum walks on general graphs
Kendon, V
2003-01-01
A scheme for a discrete time quantum walk on a general graph of N vertices with undirected edges is given, and compared with the continuous time quantum walk on a general graph introduced by Farhi and Gutmann [PRA 58 915 (1998)]. Both walks are contrasted with the examples of quantum walks in the literature treating graphs of fixed, small (< log N) degree. This illustrates the way in which extra information about the graph allows more efficient algorithms to be designed. To obtain a quantum speed up over classical for comparable resources it is necessary to code the position space of the quantum walk into a qubit register (or equivalent). The role of the oracle is also discussed and an efficient gate sequence is presented for implementing a discrete quantum walk given one copy of a quantum state encoding the adjacency matrix of the graph.
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
2005-01-01
We consider the problem of construction of graphs with given degree $k$ and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed ...... by Royle, four of the known cages including the Hoffman-Singleton graph, some graphs constructed by Exoo and some new smallest known graphs....
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G....... Royle, four of the known cages including the Hoffman-Singleton graph, some graphs constructed by G. Exoo and some new smallest known graphs. k...
Parallel Graph Transformation based on Merged Approach
Directory of Open Access Journals (Sweden)
Asmaa Aouat
2013-01-01
Full Text Available Graph transformation is one of the key concepts in graph grammar. In order to accelerate the graph transformation, the concept of parallel graph transformation has been proposed by different tools such as AGG tool. The theory of parallel graph transformation used by AGG just allows clarifying the concepts of conflict and dependency between the transformation rules. This work proposes an approach of parallel graph transformations which enables dependent transformation rules to be executed in parallel.
On characterizing terrain visibility graphs
Directory of Open Access Journals (Sweden)
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Expander Families and Cayley Graphs A Beginner's Guide
Krebs, Mike
2011-01-01
The theory of expander graphs is a rapidly developing topic in mathematics and computer science, with applications to communication networks, error-correcting codes, cryptography, complexity theory, and much more. Expander Families and Cayley Graphs: A Beginner's Guide is a comprehensive introduction to expander graphs, designed to act as a bridge between classroom study and active research in the field of expanders. It equips those with little or no prior knowledge with the skills necessary to both comprehend current research articles and begin their own research. Central to this book are fou
Periodic 2-graphs arising from subshifts
Pask, David; Weaver, Natasha
2009-01-01
Higher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz-Krieger algebras. In a previous paper, we constructed 2-graphs whose path spaces are rank-two subshifts of finite type, and showed that this construction yields aperiodic 2-graphs whose $C^*$-algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2-graphs which we call \\emph{domino graphs}. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for the $C^*$-algebras of domino graphs.
Hierarchy of modular graph identities
Energy Technology Data Exchange (ETDEWEB)
D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)
2016-11-09
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Design Pattern Mining Using Graph Matching
Institute of Scientific and Technical Information of China (English)
LI Qing-hua; ZHANG Zhi-xiang; BEN Ke-rong
2004-01-01
The identification of design pattern instances is important for program understanding and software maintenance. Aiming at the mining of design patterns in existing systems, this paper proposes a sub-graph isomorphism approach to discover several design patterns in a legacy system at a time. The attributed relational graph is used to describe design patterns and legacy systems. The sub-graph isomorphism approach consists of decomposition and composition process. During the decomposition process, graphs corresponding to the design patterns are decomposed into sub-graphs, some of which are graphs corresponding to the elemental design patterns. The composition process tries to get sub-graph isomorphism of the matched graph if sub-graph isomorphism of each sub-graph is obtained. Due to the common structures between design patterns, the proposed approach can reduce the matching times of entities and relations. Compared with the existing methods, the proposed algorithm is not linearly dependent on the number of design pattern graphs.
Acyclic edge colorings of planar graphs and series parallel graphs
Institute of Scientific and Technical Information of China (English)
HOU JianFeng; WU JianLiang; LIU GuiZhen; LIU Bin
2009-01-01
A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G.The acyclic edge chromatic number of G,denoted by a'(G),is the least number of colors in an acyclic edge coloring of G.Alon et al.conjectured that a'(G) ≤△(G) +2 for any graphs.For planar graphs G with girth g(G),we prove that a'(G) ≤ max{2△(G)-2,△(G) +22} if g(G) ≥3,a'(G)≤△(G)+2if g(G) ≥ 5,a'(G) ≤△(G)+1 if g(G) ≥ 7,and a'(G)=△(G) if g(G) ≥ 16 and △(G) ≥ 3.For series-parallel graphs G,we have a'(G) ≤ △(G) +1.
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar...
Graph Model Based Indoor Tracking
DEFF Research Database (Denmark)
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
infrastructure for different symbolic positioning technologies, e.g., Bluetooth and RFID. More specifically, the paper proposes a model of indoor space that comprises a base graph and mappings that represent the topology of indoor space at different levels. The resulting model can be used for one or several...... indoor positioning technologies. Focusing on RFID-based positioning, an RFID specific reader deployment graph model is built from the base graph model. This model is then used in several algorithms for constructing and refining trajectories from raw RFID readings. Empirical studies with implementations...
Chordal Graphs are Fully Orientable
Lai, Hsin-Hao
2012-01-01
Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying m <= d <= M. A graph G is called chordal if every cycle in G of length at least four has a chord. We show that all chordal graphs are fully orientable.
Symmetry properties of subdivision graphs
Daneshkhah, Ashraf; Devillers, Alice; Praeger, Cheryl E.
2010-01-01
The subdivision graph $S(\\Sigma)$ of a graph $\\Sigma$ is obtained from $\\Sigma$ by `adding a vertex' in the middle of every edge of $\\Si$. Various symmetry properties of $\\S(\\Sigma)$ are studied. We prove that, for a connected graph $\\Sigma$, $S(\\Sigma)$ is locally $s$-arc transitive if and only if $\\Sigma$ is $\\lceil\\frac{s+1}{2}\\rceil$-arc transitive. The diameter of $S(\\Sigma)$ is $2d+\\delta$, where $\\Sigma$ has diameter $d$ and $0\\leqslant \\delta\\leqslant 2$, and local $s$-distance transi...
Recursive processing of cyclic graphs.
Bianchini, Monica; Gori, Marco; Sarti, Lorenzo; Scarselli, Franco
2006-01-01
Recursive neural networks are a powerful tool for processing structured data. According to the recursive learning paradigm, the input information consists of directed positional acyclic graphs (DPAGs). In fact, recursive networks are fed following the partial order defined by the links of the graph. Unfortunately, the hypothesis of processing DPAGs is sometimes too restrictive, being the nature of some real-world problems intrinsically cyclic. In this paper, a methodology is proposed, which allows us to process any cyclic directed graph. Therefore, the computational power of recursive networks is definitely established, also clarifying the underlying limitations of the model.
Cubature formulas on combinatorial graphs
Pesenson, Isaac Z
2011-01-01
Many contemporary applications, for example, cataloging of galaxies, document analysis, face recognition, learning theory, image processing, operate with a large amount of data which is often represented as a graph embedded into a high dimensional Euclidean space. The variety of problems arising in contemporary data processing requires development on graphs such topics of the classical harmonic analysis as Shannon sampling, splines, wavelets, cubature formulas. The goal of the paper is to establish cubature formulas on finite combinatorial graphs. The results have direct applications to problems that arise in connection with data filtering, data denoising and data dimension reduction.
On Dominator Colorings in Graphs
Indian Academy of Sciences (India)
S Arumugam; Jay Bagga; K Raja Chandrasekar
2012-11-01
A dominator coloring of a graph is a proper coloring of in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of is called the dominator chromatic number of and is denoted by $ d(G)$. In this paper we present several results on graphs with $ d(G)=(G)$ and $ d(G)=(G)$ where $(G)$ and $(G)$ denote respectively the chromatic number and the domination number of a graph . We also prove that if $(G)$ is the Mycielskian of , then $ d(G)+1≤ d((G))≤ d(G)+2$.
Multigraph: Reusable Interactive Data Graphs
Phillips, M. B.
2010-12-01
There are surprisingly few good software tools available for presenting time series data on the internet. The most common practice is to use a desktop program such as Excel or Matlab to save a graph as an image which can be included in a web page like any other image. This disconnects the graph from the data in a way that makes updating a graph with new data a cumbersome manual process, and it limits the user to one particular view of the data. The Multigraph project defines an XML format for describing interactive data graphs, and software tools for creating and rendering those graphs in web pages and other internet connected applications. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions; the user can pan and zoom by clicking and dragging, in a familiar "Google Maps" kind of way. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf" through large data sets, downloading only those the parts of the data that are needed for display. The Multigraph XML format, or "MUGL" for short, provides a concise description of the visual properties of a graph, such as axes, plot styles, data sources, labels, etc, as well as interactivity properties such as how and whether the user can pan or zoom along each axis. Multigraph reads a file in this format, draws the described graph, and allows the user to interact with it. Multigraph software currently includes a Flash application for embedding graphs in web pages, a Flex component for embedding graphs in larger Flex/Flash applications, and a plugin for creating graphs in the WordPress content management system. Plans for the future include a Java version for desktop viewing and editing, a command line version for batch and server side rendering, and possibly Android and iPhone versions. Multigraph is currently in use on several web
Mutual Contextualization in Tripartite Graphs of Folksonomies
Yeung, Ching-Man Au; Gibbins, Nicholas; Shadbolt, Nigel
The use of tags to describe Web resources in a collaborative manner has experienced rising popularity among Web users in recent years. The product of such activity is given the name folksonomy, which can be considered as a scheme of organizing information in the users' own way. This research work attempts to analyze tripartite graphs - graphs involving users, tags and resources - of folksonomies and discuss how these elements acquire their semantics through their associations with other elements, a process we call mutual contextualization. By studying such process, we try to identify solutions to problems such as tag disambiguation, retrieving documents of similar topics and discovering communities of users. This paper describes the basis of the research work, mentions work done so far and outlines future plans.
Total Restrained Bondage in Graphs
Institute of Scientific and Technical Information of China (English)
Nader JAFARI RAD; Roslan HASNI; Joanna RACZEK; Lutz VOLKMANN
2013-01-01
A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V(G)-S is also adjacent to a vertex in V(G)-S.The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G.In this paper we initiate the study of total restrained bondage in graphs.The total restrained bondage number in a graph G with no isolated vertex,is the minimum cardinality of a subset of edges E such that G-E has no isolated vertex and the total restrained domination number of G-E is greater than the total restrained domination number of G.We obtain several properties,exact values and bounds for the total restrained bondage number of a graph.
Digital Line Graph - Large Scale
U.S. Geological Survey, Department of the Interior — Digital line graph (DLG) data are digital representations of cartographic information. DLGs of map features are converted to digital form from maps and related...
Digital Line Graph - Large Scale
U.S. Geological Survey, Department of the Interior — Digital line graph (DLG) data are digital representations of cartographic information. DLGs of map features are converted to digital form from maps and related...
Hierarchical clustering for graph visualization
Clémençon, Stéphan; Rossi, Fabrice; Tran, Viet Chi
2012-01-01
This paper describes a graph visualization methodology based on hierarchical maximal modularity clustering, with interactive and significant coarsening and refining possibilities. An application of this method to HIV epidemic analysis in Cuba is outlined.
Chordal Graphs and Semidefinite Optimization
DEFF Research Database (Denmark)
Vandenberghe, Lieven; Andersen, Martin Skovgaard
2015-01-01
in combinatorial optimization, linear algebra, statistics, signal processing, machine learning, and nonlinear optimization. This survey covers the theory and applications of chordal graphs, with an emphasis on algorithms developed in the literature on sparse Cholesky factorization. These algorithms are formulated......Chordal graphs play a central role in techniques for exploiting sparsity in large semidefinite optimization problems and in related con-vex optimization problems involving sparse positive semidefinite matrices. Chordal graph properties are also fundamental to several classical results...... as recursions on elimination trees, supernodal elimination trees, or clique trees associated with the graph. The best known example is the multifrontal Cholesky factorization algorithm, but similar algorithms can be formulated for a variety of related problems, including the computation of the partial inverse...
Baillie, C F; Kownacki, J P
1994-01-01
The Ising model on ``thin'' graphs (standard Feynman diagrams) displays several interesting properties. For ferromagnetic couplings there is a mean field phase transition at the corresponding Bethe lattice transition point. For antiferromagnetic couplings the replica trick gives some evidence for a spin glass phase. In this paper we investigate both the ferromagnetic and antiferromagnetic models with the aid of simulations. We confirm the Bethe lattice values of the critical points for the ferromagnetic model on \\phi^3 and \\phi^4 graphs and examine the putative spin glass phase in the antiferromagnetic model by looking at the overlap between replicas in a quenched ensemble of graphs. We also compare the Ising results with those for higher state Potts models and Ising models on ``fat'' graphs, such as those used in 2D gravity simulations.
Open Graphs and Computational Reasoning
Directory of Open Access Journals (Sweden)
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Tree decompositions and social graphs
Adcock, Aaron B; Mahoney, Michael W
2014-01-01
Recent work has established that large informatics graphs such as social and information networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we present results from the first detailed empirical evaluation of the use of tree decomposition (TD) heuristics for structure identification and extraction in social graphs. Although TDs have historically been used in structural graph theory and scientific computing, we show that---even with existing TD heuristics developed for those very different areas---TD methods can identify interesting structure in a wide range of realistic informatics graphs. Among other things, we show that TD methods can identify structures that correlate strongly with the core-periphery structure of realistic networks, even when using simple greedy heuristics; we show that the peripheral bags of these TDs correlate well with low-conductance communities (when they exist) found using local spectral computations; and we show that several types of large-scale "...
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Exploration of Periodically Varying Graphs
Flocchini, Paola; Santoro, Nicola
2009-01-01
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers. These graphs naturally model highly dynamic infrastructure-less networks such as public transports with fixed timetables, low earth orbiting (LEO) satellite systems, security guards' tours, etc. We establish necessary conditions for the problem to be solved. We also derive lower bounds on the amount of time required in general, as well as for the PV graphs defined by restricted classes of carriers movements: simple routes, and circular routes. We then prove that the limitations on computability and complexity we have established are indeed tight. In fact we prove that all necessary conditions are also sufficient and all lower bounds on costs are tight. We do so constructively presenting two worst case optimal solution algorithms, one for anonymous systems, and one for those w...
Connectivity threshold for Bluetooth graphs
Broutin, Nicolas; Fraiman, Nicolas; Lugosi, Gábor
2011-01-01
We study the connectivity properties of random Bluetooth graphs that model certain "ad hoc" wireless networks. The graphs are obtained as "irrigation subgraphs" of the well-known random geometric graph model. There are two parameters that control the model: the radius $r$ that determines the "visible neighbors" of each node and the number of edges $c$ that each node is allowed to send to these. The randomness comes from the underlying distribution of data points in space and from the choices of each vertex. We prove that no connectivity can take place with high probability for a range of parameters $r, c$ and completely characterize the connectivity threshold (in $c$) for values of $r$ close the critical value for connectivity in the underlying random geometric graph.
Rank of Stably Dissipative Graphs
Duarte, Pedro
2011-01-01
For the class of stably dissipative Lotka-Volterra systems we prove that the rank of its defining matrix, which is the dimension of the associated invariant foliation, is completely determined by the system's graph.
Special Issue on Graph Algorithms
2013-01-01
This special issue of Algorithms is devoted to the design and analysis of algorithms for solving combinatorial problems of a theoretical or practical nature involving graphs, with a focus on computational complexity.
Graph Model Based Indoor Tracking
DEFF Research Database (Denmark)
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...... infrastructure for different symbolic positioning technologies, e.g., Bluetooth and RFID. More specifically, the paper proposes a model of indoor space that comprises a base graph and mappings that represent the topology of indoor space at different levels. The resulting model can be used for one or several...... indoor positioning technologies. Focusing on RFID-based positioning, an RFID specific reader deployment graph model is built from the base graph model. This model is then used in several algorithms for constructing and refining trajectories from raw RFID readings. Empirical studies with implementations...
Algorithms for Comparing Pedigree Graphs
Kirkpatrick, Bonnie; Finucane, Hilary; Jiang, Haitao; Zhu, Binhai; Karp, Richard M
2010-01-01
Pedigree graphs, which represent family relationships, are often constructed by collecting data from genealogical records to determine which pairs of people are parent and child. This process is expensive, and small mistakes in data collection--for example, one missing parent-child relationship--can cause large differences in the pedigree graphs created. In this paper, we introduce a simple pedigree definition based on a different type of data which is potentially easier to collect. This alternative characterization of a pedigree that describes a pedigree as a list of the descendants of each individual, rather than a list of parent-child relationships. We then introduce an algorithm that generates the pedigree graph from this list of descendants. We also consider the problem of comparing two pedigree graphs, which could be useful to evaluate the differences between pedigrees constructed via different methods. Specifically, this could be useful to evaluate pedigree reconstruction methods. We define the edit di...
Some Graphs Containing Unique Hamiltonian Cycles
Lynch, Mark A. M.
2002-01-01
In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Hard graphs for the maximum clique problem
Hoede, Cornelis
1988-01-01
The maximum clique problem is one of the NP-complete problems. There are graphs for which a reduction technique exists that transforms the problem for these graphs into one for graphs with specific properties in polynomial time. The resulting graphs do not grow exponentially in order and number. Gra
Generalized wreath products of graphs and groups
Donno, Alfredo
2013-01-01
Inspired by the definition of generalized wreath product of permutation groups, we define the generalized wreath product of graphs, containing the classical Cartesian and wreath product of graphs as particular cases. We prove that the generalized wreath product of Cayley graphs of finite groups is the Cayley graph of the generalized wreath product of the corresponding groups.
Graphs whose complement and square are isomorphic
DEFF Research Database (Denmark)
Milanic, M.; Pedersen, Anders Sune; Pellicer, D.;
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square...
Subgraph conditions for Hamiltonian properties of graphs
Li, Binlong; Li, Binlong
2012-01-01
The research that forms the basis of this thesis addresses the following general structural questions in graph theory: which fixed graph of pair of graphs do we have to forbid as an induced subgraph of an arbitrary graph G to guarantee that G has a nice structure? In this thesis the nice structural
Chain graph models and their causal interpretations
DEFF Research Database (Denmark)
Lauritzen, Steffen Lilholt; Richardson, Thomas S.
2002-01-01
Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are many simple and apparently plausible, but ultimately fallaciou...
Localized endomorphisms of graph algebras
Conti, Roberto; Szymanski, Wojciech
2011-01-01
Endomorphisms of graph C*-algebras are investigated. A combinatorial approach to analysis of permutative endomorphisms is developed. Then invertibility criteria for localized endomorphisms are given. Furthermore, proper endomorphisms which restrict to automorphisms of the canonical diagonal MASA are analyzed. The Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. Criteria of outerness for automorphisms in the restricted Weyl group are found.
Fundamental cycles and graph embeddings
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, we investigate fundamental cycles in a graph G and their relations with graph embeddings. We show that a graph G may be embedded in an orientable surface with genus at least g if and only if for any spanning tree T , there exists a sequence of fundamental cycles C1, C2, . . . , C2g with C2i-1 ∩ C2i≠ф for 1≤ i ≤g. In particular, among β(G) fundamental cycles of any spanning tree T of a graph G, there are exactly 2γM (G) cycles C1, C2, . . . , C2γM (G) such that C2i-1 ∩ C2i≠ф for 1 ≤i≤γM (G), where β(G) and γM (G) are the Betti number and the maximum genus of G, respectively. This implies that it is possible to construct an orientable embedding with large genus of a graph G from an arbitrary spanning tree T (which may have very large number of odd components in G\\E(T )). This is different from the earlier work of Xuong and Liu, where spanning trees with small odd components are needed. In fact, this makes a common generalization of Xuong, Liu and Fu et al. Furthermore, we show that (1) this result is useful for locating the maximum genus of a graph having a specific edge-cut. Some known results for embedded graphs are also concluded; (2) the maximum genus problem may be reduced to the maximum matching problem. Based on this result and the algorithm of Micali-Vazirani, we present a new efficient algorithm to determine the maximum genus of a graph in O((β(G)) 25 ) steps. Our method is straight and quite different from the algorithm of Furst, Gross and McGeoch which depends on a result of Giles where matroid parity method is needed.
Behavior of Graph Laplacians on Manifolds with Boundary
Zhou, Xueyuan
2011-01-01
In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the convergence of graph Laplacians obtained from sampled data to certain continuous operators has become an active research topic recently. Most of the existing work has been done under the assumption that the data is sampled from a manifold without boundary or that the functions of interests are evaluated at a point away from the boundary. However, the question of boundary behavior is of considerable practical and theoretical interest. In this paper we provide an analysis of the behavior of graph Laplacians at a point near or on the boundary, discuss their convergence rates and their implications and provide some numerical results. It turns out that while points near the boundary occupy only a small part of the total volume of a manifold, the behavior of graph Laplacian there has different scaling properties from its beh...
Cycle-maximal triangle-free graphs
DEFF Research Database (Denmark)
Durocher, Stephane; Gunderson, David S.; Li, Pak Ching
2015-01-01
Abstract We conjecture that the balanced complete bipartite graph K ⌊ n / 2 ⌋ , ⌈ n / 2 ⌉ contains more cycles than any other n -vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds...... on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing...
The Rank of Integral Circulant Graphs
Institute of Scientific and Technical Information of China (English)
ZHOU Hou-qing
2014-01-01
A graph is called an integral graph if it has an integral spectrum i.e., all eigen-values are integers. A graph is called circulant graph if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. The rank of a graph is defined to be the rank of its adjacency matrix. This importance of the rank, due to applications in physics, chemistry and combinatorics. In this paper, using Ramanujan sums, we study the rank of integral circulant graphs and gave some simple computational formulas for the rank and provide an example which shows the formula is sharp.
Color Energy Of A Unitary Cayley Graph
Directory of Open Access Journals (Sweden)
Adiga Chandrashekar
2014-11-01
Full Text Available Let G be a vertex colored graph. The minimum number χ(G of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G and computed the color energy of few families of graphs with χ(G colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xnc and some gcd-graphs.
Weak Total Resolvability In Graphs
Directory of Open Access Journals (Sweden)
Casel Katrin
2016-02-01
Full Text Available A vertex v ∈ V (G is said to distinguish two vertices x, y ∈ V (G of a graph G if the distance from v to x is di erent from the distance from v to y. A set W ⊆ V (G is a total resolving set for a graph G if for every pair of vertices x, y ∈ V (G, there exists some vertex w ∈ W − {x, y} which distinguishes x and y, while W is a weak total resolving set if for every x ∈ V (G−W and y ∈ W, there exists some w ∈ W −{y} which distinguishes x and y. A weak total resolving set of minimum cardinality is called a weak total metric basis of G and its cardinality the weak total metric dimension of G. Our main contributions are the following ones: (a Graphs with small and large weak total metric bases are characterised. (b We explore the (tight relation to independent 2-domination. (c We introduce a new graph parameter, called weak total adjacency dimension and present results that are analogous to those presented for weak total dimension. (d For trees, we derive a characterisation of the weak total (adjacency metric dimension. Also, exact figures for our parameters are presented for (generalised fans and wheels. (e We show that for Cartesian product graphs, the weak total (adjacency metric dimension is usually pretty small. (f The weak total (adjacency dimension is studied for lexicographic products of graphs.
Graph Signatures for Visual Analytics
Energy Technology Data Exchange (ETDEWEB)
Wong, Pak C.; Foote, Harlan P.; Chin, George; Mackey, Patrick S.; Perrine, Kenneth A.
2006-11-17
We present a visual analytics technique to explore graphs using the concept of a data signature. A data signature, in our context, is a multidimensional vector that captures the local topology information surrounding each graph node. Signature vectors extracted from a graph are projected onto a low-dimensional scatterplot through the use of scaling. The resultant scatterplot, which reflects the similarities of the vectors, allows analysts to examine the graph structures and their corresponding real-life interpretations through repeated use of brushing and linking between the two visualizations. The interpretation of the graph structures is based on the outcomes of multiple participatory analysis sessions with intelligence analysts conducted by the authors at the Pacific Northwest National Laboratory. The paper first uses three public domain datasets with either well-known or obvious features to explain the rationale of our design and illustrate its results. More advanced examples are then used in a customized usability study to evaluate the effectiveness and efficiency of our approach. The study results reveal not only the limitations and weaknesses of the traditional approach based solely on graph visualization but also the advantages and strengths of our signature-guided approach presented in the paper.
Information Spreading in Dynamic Graphs
Clementi, Andrea; Trevisan, Luca
2011-01-01
We present a general approach to study the flooding time (a measure of how fast information spreads) in dynamic graphs (graphs whose topology changes with time according to a random process). We consider arbitrary converging Markovian dynamic graph process, that is, processes in which the topology of the graph at time $t$ depends only on its topology at time $t-1$ and which have a unique stationary distribution. The most well studied models of dynamic graphs are all Markovian and converging. Under general conditions, we bound the flooding time in terms of the mixing time of the dynamic graph process. We recover, as special cases of our result, bounds on the flooding time for the \\emph{random trip} model and the \\emph{random path} models; previous analysis techniques provided bounds only in restricted settings for such models. Our result also provides the first bound for the \\emph{random waypoint} model (which is tight for certain ranges of parameters) whose analysis had been an important open question.
Chromatic polynomials of random graphs
Van Bussel, Frank; Ehrlich, Christoph; Fliegner, Denny; Stolzenberg, Sebastian; Timme, Marc
2010-04-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Directory of Open Access Journals (Sweden)
Nilanjan De
2014-01-01
Full Text Available The connective eccentric index of a graph is a topological index involving degrees and eccentricities of vertices of the graph. In this paper, we have studied the connective eccentric index for double graph and double cover. Also we give the connective eccentric index for some graph operations such as joins, symmetric difference, disjunction, and splice of graphs.
On P-transitive graphs and applications
Directory of Open Access Journals (Sweden)
Giacomo Lenzi
2011-06-01
Full Text Available We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu-calculus fixpoint hierarchy is infinite for P-transitive graphs. Both results contrast with the case of transitive graphs. We give also an undecidability result for an enriched mu-calculus on P-transitive graphs. Finally, we consider a polynomial time reduction from the model checking problem on arbitrary graphs to the model checking problem on P-transitive graphs. All these results carry over to 3-transitive graphs.
Directory of Open Access Journals (Sweden)
Ullas Thomas
2015-07-01
Full Text Available This paper contains certain properties of set-magic graphs and obtained the set-magic number of certain classes of graphs. All spanning super graphs of a set-magic graph always set-magic and all cycles and Hamiltonian graphs are set-magic. Also set-magic number of any cycle of size 2n is always greater than n.
The Clique Problem in Ray Intersection Graphs
Cabello, Sergio; Langerman, Stefan
2011-01-01
Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph. The construction can be done in polynomial time and implies that finding a maximum clique in a segment intersection graph is NP-hard. This solves a 21-year old open problem posed by Kratochv\\'il and Ne\\v{s}et\\v{r}il.
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
Directory of Open Access Journals (Sweden)
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Private Graphs - Access Rights on Graphs for Seamless Navigation
Dorner, W.; Hau, F.; Pagany, R.
2016-06-01
After the success of GNSS (Global Navigational Satellite Systems) and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS - Real Time Locating Services (e.g. WIFI) and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites), but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Complexity of Cocktail Party Graph and Crown Graph
Directory of Open Access Journals (Sweden)
S. N. Daoud
2012-01-01
Full Text Available Problem statement: The number of spanning trees τ(G in graphs (networks was an important invariant. Approach: Using the properties of the Chebyshev polynomials of the second kind and the linear algebra techniques to evaluate the associated determinants. Results: The complexity, number of spanning trees, of the cocktail party graph on 2n vertices, given in detail in the text was proved. Also the complexity of the crown graph on 2n vertices was shown to had the value nn-2 (n-1 (n-2n-1. Conclusion: The number of spanning trees τ(G in graphs (networks is an important invariant. The evaluation of this number and analyzing its behavior is not only interesting from a mathematical (computational perspective, but also, it is an important measure of reliability of a network and designing electrical circuits. Some computationally hard problems such as the travelling salesman problem can be solved approximately by using spanning trees. Due to the high dependence of the network design and reliability on the graph theory we introduced the above important theorems and lemmas and their proofs.
From the Coxeter graph to the Klein graph
Dejter, Italo J
2010-01-01
We show that the 56-vertex Klein cubic graph $\\G'=F_{056}B$ (so denoted in the Foster census) can be obtained from the 28-vertex Coxeter graph $\\G=F_{028}A$ by 'zipping' adequately the squares of the 24 7-cycles of $\\G$ endowed with an orientation obtained by considering $\\G$ as a $\\mathcal C$-ultrahomogeneous digraph, where $\\mathcal C$ is the set of oriented 7-cycles $\\vec{C}_7$ and $2$-paths $\\vec{P}_3$, that tightly fasten those $\\vec{C}_7$ in $\\G$. In the process, it is seen that $\\G'$ is a ${\\mathcal C}'$-ultrahomogeneous graph, where ${\\mathcal C}'$ is the set of 7-cycles $C_7$ and $1$-paths $P_2$, that tightly fasten those $C_7$ in $\\G'$; this yields an embedding of $\\G'$ into a 3-torus $T_3$, which forms the Klein map of Coxeter notation $(7,3)_8$. The dual graph of $\\G'$ in $T_3$ is the distance regular Klein quartic graph, with corresponding dual map of Coxeter notation $(3,7)_8$.
GraphMeta: Managing HPC Rich Metadata in Graphs
Energy Technology Data Exchange (ETDEWEB)
Dai, Dong; Chen, Yong; Carns, Philip; Jenkins, John; Zhang, Wei; Ross, Robert
2016-01-01
High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introduces significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.
Subvoxel accurate graph search using non-Euclidean graph space.
Directory of Open Access Journals (Sweden)
Michael D Abràmoff
Full Text Available Graph search is attractive for the quantitative analysis of volumetric medical images, and especially for layered tissues, because it allows globally optimal solutions in low-order polynomial time. However, because nodes of graphs typically encode evenly distributed voxels of the volume with arcs connecting orthogonally sampled voxels in Euclidean space, segmentation cannot achieve greater precision than a single unit, i.e. the distance between two adjoining nodes, and partial volume effects are ignored. We generalize the graph to non-Euclidean space by allowing non-equidistant spacing between nodes, so that subvoxel accurate segmentation is achievable. Because the number of nodes and edges in the graph remains the same, running time and memory use are similar, while all the advantages of graph search, including global optimality and computational efficiency, are retained. A deformation field calculated from the volume data adaptively changes regional node density so that node density varies with the inverse of the expected cost. We validated our approach using optical coherence tomography (OCT images of the retina and 3-D MR of the arterial wall, and achieved statistically significant increased accuracy. Our approach allows improved accuracy in volume data acquired with the same hardware, and also, preserved accuracy with lower resolution, more cost-effective, image acquisition equipment. The method is not limited to any specific imaging modality and readily extensible to higher dimensions.
Roman domination in Cartesian product graphs and strong product graphs
Yero, Ismael G
2011-01-01
A set $S$ of vertices of a graph $G$ is a dominating set for $G$ if every vertex outside of $S$ is adjacent to at least one vertex belonging to $S$. The minimum cardinality of a dominating set for $G$ is called the domination number of $G$. A map $f : V \\rightarrow \\{0, 1, 2\\}$ is a Roman dominating function on a graph $G$ if for every vertex $v$ with $f(v) = 0$, there exists a vertex $u$, adjacent to $v$, such that $f(u) = 2$. The weight of a Roman dominating function is given by $f(V) =\\sum_{u\\in V}f(u)$. The minimum weight of a Roman dominating function on $G$ is called the Roman domination number of $G$. In this article we study the Roman domination number of Cartesian product graphs and strong product graphs. More precisely, we study the relationships between the Roman domination number of product graphs and the (Roman) domination number of the factors.
Kirchoff Index of Graphs and some Graph Operations
Indian Academy of Sciences (India)
A Nikseresht; Z Sepasdar; M H Shirdareh-Haghighi
2014-08-01
Let be a rooted tree, a connected graph, $x,y\\in V(G)$ be fixed and $G_i$’s be $|V(T)|$ disjoint copies of with $x_i$ and $y_i$ denoting the corresponding copies of and in $G_i$, respectively. We define the -repetition of to be the graph obtained by joining $y_i$ to $x_j$ for each $i\\in V(T)$ and each child of . In this paper, we compute the Kirchhoff index of the -repetition of in terms of parameters of and . Also we study how $Kf(G)$ behaves under some graph operations such as joining vertices or subdividing edges.
Collaborative mining of graph patterns from multiple sources
Levchuk, Georgiy; Colonna-Romanoa, John
2016-05-01
Intelligence analysts require automated tools to mine multi-source data, including answering queries, learning patterns of life, and discovering malicious or anomalous activities. Graph mining algorithms have recently attracted significant attention in intelligence community, because the text-derived knowledge can be efficiently represented as graphs of entities and relationships. However, graph mining models are limited to use-cases involving collocated data, and often make restrictive assumptions about the types of patterns that need to be discovered, the relationships between individual sources, and availability of accurate data segmentation. In this paper we present a model to learn the graph patterns from multiple relational data sources, when each source might have only a fragment (or subgraph) of the knowledge that needs to be discovered, and segmentation of data into training or testing instances is not available. Our model is based on distributed collaborative graph learning, and is effective in situations when the data is kept locally and cannot be moved to a centralized location. Our experiments show that proposed collaborative learning achieves learning quality better than aggregated centralized graph learning, and has learning time comparable to traditional distributed learning in which a knowledge of data segmentation is needed.
The monadic second-order logic of graphs XVI : Canonical graph
decompositions
Courcelle, Bruno
2005-01-01
This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs having the same cycle matroid as a given 2-connected graph can be defined from this graph by Monadic Se...
Anderson, Lori S; Enge, Karmin J
2012-10-01
School nurses care for children with a variety of health-related conditions and they need information about managing these conditions, which is accessible, current, and useful. The goal of this literature review was to gather and synthesize information on technology-supported resources and to determine which met the educational needs of school nurses. Successful online educational programs were interactive and self-directed. The most common barriers were lack of time to find educational information, lack of knowledge about computers, technology, the Internet and specific programs, and lack of administrative support from school officials to use technology to access information and evidence for practice. Recommendations for successful use of technology to meet practicing school nurse's educational needs are offered.
Hybrid vehicle turbine engine technology support (HVTE-TS) project. 1995--1996 annual report
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-12-31
This report presents a summary of technical work accomplished on the Hybrid Vehicle Turbine Engine--Technology Support (HVTE-TS) Project during calendar years 1995 and 1996. Work was performed under an initial National Aeronautics and Space Administration (NASA) contract DEN3-336. As of September 1996 the contract administration was transferred to the US Department of Energy (DoE) Chicago Operations Office, and renumbered as DE-AC02-96EE50553. The purpose of the HVTE-TS program is to develop gas turbine engine technology in support of DoE and automotive industry programs exploring the use of gas turbine generator sets in hybrid-electric automotive propulsion systems. The program focus is directed to the development of four key technologies to be applied to advanced turbogenerators for hybrid vehicles: Structural ceramic materials and processes; Low emissions combustion systems; Regenerators and seals systems; and Insulation systems and processes. 60 figs., 9 tabs.
The competition numbers of ternary Hamming graphs
Park, Boram
2010-01-01
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs to characterize a graph by its competition number. In this paper, we give the exact values of the competition numbers of ternary Hamming graphs.
Directory of Open Access Journals (Sweden)
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Braun, Andreas P.; Schäfer-Nameki, Sakura
2016-04-01
Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial) toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU (5) by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Algebraic connectivity and graph robustness.
Energy Technology Data Exchange (ETDEWEB)
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T. (University of New Mexico)
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
Negation switching invariant signed graphs
Directory of Open Access Journals (Sweden)
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Rosmanis, Ansis
2010-01-01
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states which most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next I discuss how an algorithm based on the quantum snake walk might be able to solve an extended version of the glued trees problem which asks to find a path connecting both roots of the glued trees graph. No efficient quantum algorithm solving this problem is known yet.
Optimal preparation of graph states
Cabello, Adan; Lopez-Tarrida, Antonio J; Portillo, Jose R
2010-01-01
We show how to prepare any graph state of up to 12 qubits with: (a) the minimum number of controlled-Z gates, and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.
Significance evaluation in factor graphs
DEFF Research Database (Denmark)
Madsen, Tobias; Hobolth, Asger; Jensen, Jens Ledet
2017-01-01
Background Factor graphs provide a flexible and general framework for specifying probability distributions. They can capture a range of popular and recent models for analysis of both genomics data as well as data from other scientific fields. Owing to the ever larger data sets encountered...... in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models. Results Two novel numerical approximations for evaluation of statistical....... Conclusions The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets...
Graph measures and network robustness
Ellens, W
2013-01-01
Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to continue to perform well when it is subject to failures or attacks. In this paper we survey a large amount of robustness measures on simple, undirected and unweighted graphs, in order to offer a tool for network administrators to evaluate and improve the robustness of their network. The measures discussed in this paper are based on the concepts of connectivity (including reliability polynomials), distance, betweenness and clustering. Some other measures are notions from spectral graph theory, more precisely, they are functions of the Laplacian eigenvalues. In addition to surveying these graph measures, the paper also contains a discussion of their functionality as a measure for topological network robustness.
The fascinating world of graph theory
Benjamin, Arthur; Zhang, Ping
2015-01-01
Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin
Recognition of Unipolar and Generalised Split Graphs
Directory of Open Access Journals (Sweden)
Colin McDiarmid
2015-02-01
Full Text Available A graph is unipolar if it can be partitioned into a clique and a disjoint union of cliques, and a graph is a generalised split graph if it or its complement is unipolar. A unipolar partition of a graph can be used to find efficiently the clique number, the stability number, the chromatic number, and to solve other problems that are hard for general graphs. We present an O(n2-time algorithm for recognition of n-vertex generalised split graphs, improving on previous O(n3-time algorithms.
Graph-based modelling in engineering
Rysiński, Jacek
2017-01-01
This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .
Some Invariants of Jahangir Graphs
Directory of Open Access Journals (Sweden)
Mobeen Munir
2017-01-01
Full Text Available In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs Jn,m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as first and second Zagreb indices, modified Zagreb index, Symmetric division index, etc. We also compute harmonic index, first and second multiple Zagreb indices and forgotten index of Jahangir graphs. Our results are extensions of many existing results.
Completely Described Undirected Graph Structure
Directory of Open Access Journals (Sweden)
G. S. Ivanova
2016-01-01
Full Text Available The objects of research are undirected graphs. The paper considers a problem of their isomorphism. A literature analysis of its solution, has shown that there is no way to define a complete graph invariant in the form of unique structural characteristics of each its vertex, which has a computational complexity of definition better than О (n 4 .The work objective is to provide the characteristics of the graph structure, which could be used to solve the problem of their isomorphism for a time better than О (n 4 . As such characteristics, the paper proposes to use the set of codes of tree roots of all the shortest - in terms of the number of edges - paths from each vertex to the others, uniquely defining the structure of each tree. It proves the theorem that it is possible to reduce the problem of isomorphism of the undirected graphs to the isomorphism problem of their splitting into the trees of all the shortest - in terms of the number of edges - paths of each vertex to the others. An algorithm to construct the shortest paths from each vertex to all others and to compute codes of their vertices has been developed. As the latter, are used Aho-codes, which find application in recognising the isomorphism of trees. The computational complexity to obtain structural characteristics of vertices has been estimated to be about О (n 3 .The pilot studies involved the full-scale experiment using the developed complex programmes to generate raw data, i.e. analytic representation of the graph with the number of vertices equal to 1200, and a programme to provide codes of the tree roots. To have an estimate of - "the worst" in terms of time - complexity of expansion algorithm of graphs into trees of the shortest paths and define the codes of their roots has been an experimentally studied how the number of tree vertices depends on the graph density. For the worst case was obtained a dependence of the number of tree vertices on the number of graph vertices
Scattering from isospectral quantum graphs
Energy Technology Data Exchange (ETDEWEB)
Band, R; Sawicki, A; Smilansky, U, E-mail: rami.band@weizmann.ac.i, E-mail: assawi@cft.edu.p, E-mail: uzy.smilansky@weizmann.ac.i [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel)
2010-10-15
Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles distributions are therefore identical. The scattering matrices are studied using a recently developed isospectral theory (Band et al 2009 J. Phys. A: Math. Theor. 42 175202 and Parzanchevski and Band 2010 J. Geom. Anal. 20 439-71). At the same time, the scattering approach offers a new insight on the mentioned isospectral construction.
Turing Automata and Graph Machines
Directory of Open Access Journals (Sweden)
Miklós Bartha
2010-06-01
Full Text Available Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by generalizing the classical Turing machine concept, so that the collection of such machines becomes an indexed monoidal algebra. On the analogy of the von Neumann data-flow computer architecture, Turing graph machines are proposed as potentially reversible low-level universal computational devices, and a truly reversible molecular size hardware model is presented as an example.
Topological Minors in Bipartite Graphs
Institute of Scientific and Technical Information of China (English)
Camino BALBUENA; Martín CER.A; Pedro GARC(I)A-V(A)ZQUEZ; Juan Carlos VALENZUELA
2011-01-01
For a bipartite graph G on m and n vertices,respectively,in its vertices classes,and for integers s and t such that 2 ≤ s ≤ t,0≤ m-s≤ n-t,andm,+n≤ 2s+t-1,we prove that if G has at least mn- (2(m - s) + n - t) edges then it contains a subdivision of the complete bipartite K(s,t) with s vertices in the m-class and t vertices in the n-class.Furthermore,we characterize the corresponding extremal bipartite graphs with mn- (2(m - s) + n - t + 1) edges for this topological Turan type problem.
Quantum walks on Cayley graphs
Energy Technology Data Exchange (ETDEWEB)
Lopez Acevedo, O [Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise, 2 Avenue Adolphe Chauvin 95302 Cergy Pontoise Cedex (France); Institut fuer Mathematik und Informatik, Ernst-Moritz-Arndt-Universitaet, Friedrich-Ludwig-Jahn Str.15a, 17487 Greifswald (Germany); Gobron, T [Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise, 2 Avenue Adolphe Chauvin 95302 Cergy Pontoise Cedex (France)
2006-01-20
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert space and consider various classes of graphs on which the structure of quantum walks may differ. We completely characterize quantum walks on free groups and present partial results on more general cases. Some examples are given including a family of quantum walks on the hypercube involving a Clifford algebra.
Computing Graph Roots Without Short Cycles
Farzad, Babak; Le, Van Bang; Tuy, Nguyen Ngoc
2009-01-01
Graph G is the square of graph H if two vertices x, y have an edge in G if and only if x, y are of distance at most two in H. Given H it is easy to compute its square H2, however Motwani and Sudan proved that it is NP-complete to determine if a given graph G is the square of some graph H (of girth 3). In this paper we consider the characterization and recognition problems of graphs that are squares of graphs of small girth, i.e. to determine if G = H2 for some graph H of small girth. The main results are the following. - There is a graph theoretical characterization for graphs that are squares of some graph of girth at least 7. A corollary is that if a graph G has a square root H of girth at least 7 then H is unique up to isomorphism. - There is a polynomial time algorithm to recognize if G = H2 for some graph H of girth at least 6. - It is NP-complete to recognize if G = H2 for some graph H of girth 4. These results almost provide a dichotomy theorem for the complexity of the recognition problem in terms of ...
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan
2012-11-19
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Chain graph models and their causal interpretations
DEFF Research Database (Denmark)
Lauritzen, Steffen Lilholt; Richardson, Thomas S.
2002-01-01
the equilibrium distributions of dynamic models with feed-back. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for directed acyclic graphs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have......Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are many simple and apparently plausible, but ultimately fallacious......, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from...
Mathematical Minute: Rotating a Function Graph
Bravo, Daniel; Fera, Joseph
2013-01-01
Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.
The thickness of amalgamations of graphs
Yang, Yan
2012-01-01
The thickness $\\theta(G)$ of a graph $G$ is the minimum number of planar spanning subgraphs into which the graph $G$ can be decomposed. As a topological invariant of a graph, it is a measurement of the closeness to planarity of a graph, and it also has important applications to VLSI design. In this paper, the thickness of graphs that are obtained by vertex-amalgamation and bar-amalgamation of any two graphs whose thicknesses are known are obtained, respectively. And the lower and upper bounds for the thickness of graphs that are obtained by edge-amalgamation and 2-vertex-amalgamation of any two graphs whose thicknesses are known are also derived, respectively.
The Laplacian eigenvalues of graphs: a survey
Zhang, Xiao-Dong
2011-01-01
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. This paper is primarily a survey of various aspects of the eigenvalues of the Laplacian matrix of a graph for the past teens. In addition, some new unpublished results and questions are concluded. Emphasis is given on classifications of the upper and lower bounds for the Laplacian eigenvalues of graphs (including some special graphs, such as trees, bipartite graphs, triangular-free graphs, cubic graphs, etc.) as a function of other graph invariants, such as degree sequence, the average 2-degree, diameter, the maximal independence number, the maximal matching number, vertex connectivity, the domination number, the number of the spanning trees, etc.
Measuring extremal dependencies in web graphs
Volkovich, Y.; Litvak, Nelli; Zwart, B.
We analyze dependencies in power law graph data (Web sample, Wikipedia sample and a preferential attachment graph) using statistical inference for multivariate regular variation. The well developed theory of regular variation is widely applied in extreme value theory, telecommunications and
Prudente, Matthew James
Given a graph G with pebbles on the vertices, we define a pebbling move as removing two pebbles from a vertex u, placing one pebble on a neighbor v, and discarding the other pebble, like a toll. The pebbling number pi( G) is the least number of pebbles needed so that every arrangement of pi(G) pebbles can place a pebble on any vertex through a sequence of pebbling moves. We introduce a new variation on graph pebbling called two-player pebbling. In this, players called the mover and the defender alternate moves, with the stipulation that the defender cannot reverse the previous move. The mover wins only if they can place a pebble on a specified vertex and the defender wins if the mover cannot. We define η(G), analogously, as the minimum number of pebbles such that given every configuration of the η( G) pebbles and every specified vertex r, the mover has a winning strategy. First, we will investigate upper bounds for η( G) on various classes of graphs and find a certain structure for which the defender has a winning strategy, no matter how many pebbles are in a configuration. Then, we characterize winning configurations for both players on a special class of diameter 2 graphs. Finally, we show winning configurations for the mover on paths using a recursive argument.
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...
Ancestral Genres of Mathematical Graphs
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Standards for Graph Algorithm Primitives
Mattson, Tim; Bader, David; Berry, Jon; Buluc, Aydin; Dongarra, Jack; Faloutsos, Christos; Feo, John; Gilbert, John; Gonzalez, Joseph; Hendrickson, Bruce; Kepner, Jeremy; Leiserson, Charles; Lumsdaine, Andrew; Padua, David; Poole, Stephen
2014-01-01
It is our view that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of a standard set of primitive building blocks. This paper is a position paper defining the problem and announcing our intention to launch an open effort to define this standard.
Memory Hierarchy Sensitive Graph Layout
Roy, Amitabha
2012-01-01
Mining large graphs for information is becoming an increasingly important workload due to the plethora of graph structured data becoming available. An aspect of graph algorithms that has hitherto not received much interest is the effect of memory hierarchy on accesses. A typical system today has multiple levels in the memory hierarchy with differing units of locality; ranging across cache lines, TLB entries and DRAM pages. We postulate that it is possible to allocate graph structured data in main memory in a way as to improve the spatial locality of the data. Previous approaches to improving cache locality have focused only on a single unit of locality, either the cache line or virtual memory page. On the other hand cache oblivious algorithms can optimise layout for all levels of the memory hierarchy but unfortunately need to be specially designed for individual data structures. In this paper we explore hierarchical blocking as a technique for closing this gap. We require as input a specification of the units...
Seidel Switching and Graph Energy
Haemers, W.H.
2012-01-01
Abstract: The energy of a graph Γ is the sum of the absolute values of the eigenvalues of the adjacency matrix of Γ. Seidel switching is an operation on the edge set of Γ. In some special cases Seidel switching does not change the spectrum, and therefore the energy. Here we investigate when Seidel s
Index theorems for quantum graphs
Fulling, S A; Wilson, J H
2007-01-01
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H =A*A, and relating the constant term to the index of A. An independent consideration provides an index f...
Fibonacci Identities, Matrices, and Graphs
Huang, Danrun
2005-01-01
General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…
Junction trees of general graphs
Institute of Scientific and Technical Information of China (English)
Xiaofei WANG; Jianhua GUO
2008-01-01
In this paper,we study the maximal prime subgraphs and their corresponding structure for any undirected graph.We introduce the notion of junction trees and investigate their structural characteristics,including junction properties,induced-subtree properties,running-intersection properties and maximum-weight spanning tree properties.Furthermore,the characters of leaves and edges on junction trees are discussed.
Affect and Graphing Calculator Use
McCulloch, Allison W.
2011-01-01
This article reports on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. DeBellis and Goldin's (2006) framework for affect as a representational system was used as a lens through which to understand the ways in which…
A Graph Calculus for Predicate Logic
Directory of Open Access Journals (Sweden)
Paulo A. S. Veloso
2013-03-01
Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.
An interactive system for drawing graphs
Marks, Joe; Shieber, Stuart; Ryall, Kathy
1996-01-01
Abstract: In spite of great advances in the automatic drawing of medium and large graphs, the tools available for drawing small graphs exquisitely (that is, with the aesthetics commonly found in professional publications and presentations) are still very primitive. Commercial tools, e.g., Claris Draw, provide minimal support for aesthetic graph layout. At the other extreme, research prototypes based on constraint methods are overly general for graph drawing. Our system improves on general con...
Cut Size Statistics of Graph Bisection Heuristics
Schreiber, G. R.; Martin, O. C.
1998-01-01
We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by ``local'' algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given...
Operations on Intuitionistic Fuzzy Graph Structures
Directory of Open Access Journals (Sweden)
Muhammad Akram
2016-12-01
Full Text Available An intuitionistic fuzzy graph structure (IFGS is a generalization of an intuitionistic fuzzy graph. The concept of intuitionistic fuzzy graph structure is introduced and investigated in this paper. Some operations including union, join, Cartesian product, cross product, lexicographic product, strong product and composition on intuitionistic fuzzy graph structures are defined and elaborated with a number of examples. Some basic properties of these operations are also presented.
Minimum Dominating Tree Problem for Graphs
Institute of Scientific and Technical Information of China (English)
LIN Hao; LIN Lan
2014-01-01
A dominating tree T of a graph G is a subtree of G which contains at least one neighbor of each vertex of G. The minimum dominating tree problem is to find a dominating tree of G with minimum number of vertices, which is an NP-hard problem. This paper studies some polynomially solvable cases, including interval graphs, Halin graphs, special outer-planar graphs and others.
Noncommutative Manifolds from Graph and k-Graph C*-Algebras
Pask, David; Rennie, Adam; Sims, Aidan
2009-12-01
In [PRen] we constructed smooth (1, ∞)-summable semifinite spectral triples for graph algebras with a faithful trace, and in [PRS] we constructed ( k, ∞)-summable semifinite spectral triples for k-graph algebras. In this paper we identify classes of graphs and k-graphs which satisfy a version of Connes’ conditions for noncommutative manifolds.
Implicit Hamiltonian formulation of bond graphs
Golo, G.; Schaft, A.J. van der; Breedveld, P.C.; Maschke, B.M.
2003-01-01
This paper deals with mathematical formulation of bond graphs. It is proven that the power continuous part of bond graphs, the junction structure, can be associated with a Dirac structure and that equations describing a bond graph model correspond to an implicit port-controlled Hamiltonian system wi
Cycle-maximal triangle-free graphs
DEFF Research Database (Denmark)
Durocher, Stephane; Gunderson, David S.; Li, Pak Ching;
2015-01-01
Abstract We conjecture that the balanced complete bipartite graph K ⌊ n / 2 ⌋ , ⌈ n / 2 ⌉ contains more cycles than any other n -vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds...
Around the Sun in a Graphing Calculator.
Demana, Franklin; Waits, Bert K.
1989-01-01
Discusses the use of graphing calculators for polar and parametric equations. Presents eight lines of the program for the graph of a parametric equation and 11 lines of the program for a graph of a polar equation. Illustrates the application of the programs for planetary motion and free-fall motion. (YP)
Convergence of zeta functions of graphs
Clair, Bryan; Mokhtari-Sharghi, Shahriar
2000-01-01
The $L^2$-zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta functions of the finite graphs converge to the $L^2$-zeta function of Y.
Strongly 2-connected orientations of graphs
DEFF Research Database (Denmark)
Thomassen, Carsten
2014-01-01
We prove that a graph admits a strongly 2-connected orientation if and only if it is 4-edge-connected, and every vertex-deleted subgraph is 2-edge-connected. In particular, every 4-connected graph has such an orientation while no cubic 3-connected graph has such an orientation....
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo
2009-01-01
In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.
2009-01-01
In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax
Mathematical Foundations of the GraphBLAS
Kepner, Jeremy; Bader, David; Buluc, Aydın; Franchetti, Franz; Gilbert, John; Hutchison, Dylan; Kumar, Manoj; Lumsdaine, Andrew; Meyerhenke, Henning; McMillan, Scott; Moreira, Jose; Owens, John D; Yang, Carl; Zalewski, Marcin; Mattson, Timothy
2016-01-01
The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix mul- tiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effecti...
Well-covered graphs and factors
DEFF Research Database (Denmark)
Randerath, Bert; Vestergaard, Preben D.
2006-01-01
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...
Extremal norms of graphs and matrices
Nikiforov, Vladimir
2010-01-01
In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. In this paper some of this research is extended to more general matrix norms, like the Schatten p-norms and the Ky Fan k-norms. Whenever possible the results are given both for graphs and general matrices.
Graph Partitioning Models for Parallel Computing
Energy Technology Data Exchange (ETDEWEB)
Hendrickson, B.; Kolda, T.G.
1999-03-02
Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.
2009-01-01
In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo
2009-01-01
In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java synta
Destroying longest cycles in graphs and digraphs
DEFF Research Database (Denmark)
Van Aardt, Susan A.; Burger, Alewyn P.; Dunbar, Jean E.;
2015-01-01
In 1978, C. Thomassen proved that in any graph one can destroy all the longest cycles by deleting at most one third of the vertices. We show that for graphs with circumference k≤8 it suffices to remove at most 1/k of the vertices. The Petersen graph demonstrates that this result cannot be extende...
On chromatic and flow polynomial unique graphs
National Research Council Canada - National Science Library
Duan, Yinghua; Wu, Haidong; Yu, Qinglin
2008-01-01
... research on graphs uniquely determined by their chromatic polynomials and more recently on their Tutte polynomials, but rather spotty research on graphs uniquely determined by their flow polynomials or the combination of both chromatic and flow polynomials. This article is an initiation of investigation on graphs uniquely determin...
LARGEST EIGENVALUE OF A UNICYCLIC MIXED GRAPH
Institute of Scientific and Technical Information of China (English)
FanYizheng
2004-01-01
The graphs which maximize and minimize respectively the largest eigenvalue over all unicyclic mixed graphs U on n vertices are determined. The unicyclic mixed graphs U with the largest eigenvalue λ1 (U)=n or λ1 (U)∈ (n ,n+1] are characterized.
DEFF Research Database (Denmark)
Sandborg-Petersen, Ulrik
2007-01-01
Automatically transforming text to conceptual graphs has long been a goal of the Conceptual Graphs community, starting with Sowa and Way’s seminal paper in 1986. We have developed a method for transforming Old Testament texts in Hebrew into English-based conceptual graphs, and in this paper, we r...
The Cyclic Graph of a Finite Group
Directory of Open Access Journals (Sweden)
Xuan Long Ma
2013-01-01
and characterize certain finite groups whose cyclic graphs have some properties. Then, we present some properties of the cyclic graphs of the dihedral groups D2n and the generalized quaternion groups Q4n for some n. Finally, we present some parameters about the cyclic graphs of finite noncyclic groups of order up to 14.
A new characterization of trivially perfect graphs
Directory of Open Access Journals (Sweden)
Christian Rubio Montiel
2015-03-01
Full Text Available A graph $G$ is \\emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number $\\alpha(G$ equals the number of (maximal cliques $m(G$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.
Structural intervention distance for evaluating causal graphs
DEFF Research Database (Denmark)
Peters, Jonas; Bühlmann, Peter
2015-01-01
Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-)metric between DAGs, the structural interventi...... implementation with software code available on the first author's home page....
McMillen, Sue; McMillen, Beth
2010-01-01
Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…
Integral complete r-partite graphs
Wang, Ligong; Li, Xueliang; Hoede, C.
2004-01-01
A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that
A new cluster algorithm for graphs
Dongen, S. van
1998-01-01
A new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a canonical way with
Institute of Scientific and Technical Information of China (English)
Shuhe; PU; Fuyou; WANG
2014-01-01
The current situation of the recreational agriculture development in Hainan was analyzed. The problems of imperfect security system,unsound policies and regulations,scant government support,low enthusiasm for developing recreational agriculture,lacking science and technology support and less special competitive products in Hainan were discussed. Through the reference of foreign countries and Taiwan Area policy support and legislative experience on recreational agriculture,it was recommended to perfect the policy system,develop the leading role of the government,enhance the legislation and supervision,pay attention to science and technology support,in order to promote the healthy sustainable development of recreational agriculture in Hainan.
Directory of Open Access Journals (Sweden)
Al-Mamoori Amal Ghalib Rashid
2015-01-01
Full Text Available This paper investigates the relationships among organizational structure, technological support, knowledge sharing and process innovation and whether knowledge sharing has a mediating effect on these relationships. Based on the survey among employees in the Iraqi textile industry, the results revealed that organizational structure and technological support positively and significantly influence knowledge sharing. Knowledge sharing was also found to be an important mediator between organizational structure, support technology and process innovation. The findings bear implications to the Iraqi government’s call for innovation in the Iraqi textile industry.
Directory of Open Access Journals (Sweden)
Dorel PARASCHIV
2008-01-01
Full Text Available The viability and success of modern enterprises are subject to the increasing dynamic of the economic environment, so they need to adjust rapidly their policies and strategies in order to respond to sophistication of competitors, customers and suppliers, globalization of business, international competition. Perhaps the most critical component for success of the modern enterprise is its ability to take advantage of all available information - both internal and external. Making sense of all this information, gaining value and competitive advantage through represents real challenges for the enterprise. The IT solutions designed to address these challenges have been developed in two different approaches: structured data management (Business Intelligence and unstructured content management (Knowledge Management. Integrating Business Intelligence and Knowledge Management in new software applications designated not only to store highly structured data and exploit it in real time but also to interpret the results and communicate them to decision factors provides real technological support for Strategic Management. Integrating Business Intelligence and Knowledge Management in order to respond to the challenges the modern enterprise has to deal with represents not only a "new trend" in IT, but a necessity in the emerging knowledge based economy. These hybrid technologies are already widely known in both scientific and practice communities as Competitive Intelligence. In the end of paper,a competitive datawarehouse design is proposed, in an attempt to apply business intelligence technologies to economic environment analysis making use of romanian public data sources.
Directory of Open Access Journals (Sweden)
Maher Ben-Moussa
2017-04-01
Full Text Available The present paper explores the benefits and the capabilities of various emerging state-of-the-art interactive 3D and Internet of Things technologies and investigates how these technologies can be exploited to develop a more effective technology supported exposure therapy solution for social anxiety disorder. “DJINNI” is a conceptual design of an in vivo augmented reality (AR exposure therapy mobile support system that exploits several capturing technologies and integrates the patient’s state and situation by vision-based, audio-based, and physiology-based analysis as well as by indoor/outdoor localization techniques. DJINNI also comprises an innovative virtual reality exposure therapy system that is adaptive and customizable to the demands of the in vivo experience and therapeutic progress. DJINNI follows a gamification approach where rewards and achievements are utilized to motivate the patient to progress in her/his treatment. The current paper reviews the state of the art of technologies needed for such a solution and recommends how these technologies could be integrated in the development of an individually tailored and yet feasible and effective AR/virtual reality-based exposure therapy. Finally, the paper outlines how DJINNI could be part of classical cognitive behavioral treatment and how to validate such a setup.
Ben-Moussa, Maher; Rubo, Marius; Debracque, Coralie; Lange, Wolf-Gero
2017-01-01
The present paper explores the benefits and the capabilities of various emerging state-of-the-art interactive 3D and Internet of Things technologies and investigates how these technologies can be exploited to develop a more effective technology supported exposure therapy solution for social anxiety disorder. "DJINNI" is a conceptual design of an in vivo augmented reality (AR) exposure therapy mobile support system that exploits several capturing technologies and integrates the patient's state and situation by vision-based, audio-based, and physiology-based analysis as well as by indoor/outdoor localization techniques. DJINNI also comprises an innovative virtual reality exposure therapy system that is adaptive and customizable to the demands of the in vivo experience and therapeutic progress. DJINNI follows a gamification approach where rewards and achievements are utilized to motivate the patient to progress in her/his treatment. The current paper reviews the state of the art of technologies needed for such a solution and recommends how these technologies could be integrated in the development of an individually tailored and yet feasible and effective AR/virtual reality-based exposure therapy. Finally, the paper outlines how DJINNI could be part of classical cognitive behavioral treatment and how to validate such a setup.
Bars, Lines, & Pies: A Graphing Skills Program. Expect the Unexpected with Math[R
Actuarial Foundation, 2013
2013-01-01
"Bars, Lines, & Pies" is a dynamic math program designed to build graphing skills in students, while also showing them the relevance of math in their lives. Developed by The Actuarial Foundation along with Scholastic, the graphing lessons and activities involve engaging, real-world examples about the environment and recycling. In these lessons,…
Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes
Directory of Open Access Journals (Sweden)
Katona Gyula Y.
2014-11-01
Full Text Available The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.
On a conjecture concerning helly circle graphs
Directory of Open Access Journals (Sweden)
Durán Guillermo
2003-01-01
Full Text Available We say that G is an e-circle graph if there is a bijection between its vertices and straight lines on the cartesian plane such that two vertices are adjacent in G if and only if the corresponding lines intersect inside the circle of radius one. This definition suggests a method for deciding whether a given graph G is an e-circle graph, by constructing a convenient system S of equations and inequations which represents the structure of G, in such a way that G is an e-circle graph if and only if S has a solution. In fact, e-circle graphs are exactly the circle graphs (intersection graphs of chords in a circle, and thus this method provides an analytic way for recognizing circle graphs. A graph G is a Helly circle graph if G is a circle graph and there exists a model of G by chords such that every three pairwise intersecting chords intersect at the same point. A conjecture by Durán (2000 states that G is a Helly circle graph if and only if G is a circle graph and contains no induced diamonds (a diamond is a graph formed by four vertices and five edges. Many unsuccessful efforts - mainly based on combinatorial and geometrical approaches - have been done in order to validate this conjecture. In this work, we utilize the ideas behind the definition of e-circle graphs and restate this conjecture in terms of an equivalence between two systems of equations and inequations, providing a new, analytic tool to deal with it.
A Review on Large Scale Graph Processing Using Big Data Based Parallel Programming Models
Directory of Open Access Journals (Sweden)
Anuraj Mohan
2017-02-01
Full Text Available Processing big graphs has become an increasingly essential activity in various fields like engineering, business intelligence and computer science. Social networks and search engines usually generate large graphs which demands sophisticated techniques for social network analysis and web structure mining. Latest trends in graph processing tend towards using Big Data platforms for parallel graph analytics. MapReduce has emerged as a Big Data based programming model for the processing of massively large datasets. Apache Giraph, an open source implementation of Google Pregel which is based on Bulk Synchronous Parallel Model (BSP is used for graph analytics in social networks like Facebook. This proposed work is to investigate the algorithmic effects of the MapReduce and BSP model on graph problems. The triangle counting problem in graphs is considered as a benchmark and evaluations are made on the basis of time of computation on the same cluster, scalability in relation to graph and cluster size, resource utilization and the structure of the graph.
A new construction for vertex decomposable graphs
Directory of Open Access Journals (Sweden)
Nasser Hajisharifi
2016-09-01
Full Text Available Let G be a finite simple graph on the vertex set V(G and let S⊆V(G. Adding a whisker to G at x means adding a new vertex y and edge xy to G where x∈V(G. The graph G∪W(S is obtained from G by adding a whisker to every vertex of S. We prove that if G∖S is either a graph with no chordless cycle of length other than 3 or 5, chordal graph or C5, then G∪W(S is a vertex decomposable graph.
Graph inverse semigroups: their characterization and completion
Jones, David G
2011-01-01
Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C*-algebras. This paper has two main goals: first, to provide an abstract characterization of graph inverse semigroups; and second, to show how they may be completed, under suitable conditions, to form what we call the Cuntz-Krieger semigroup of the graph. This semigroup is the ample semigroup of a topological groupoid associated with the graph, and the semigroup analogue of the Leavitt path algebra of the graph.
Line graphs and $2$-geodesic transitivity
Devillers, Alice; Jin, Wei; Li, Cai Heng; Praeger, Cheryl E.
2012-01-01
For a graph $\\Gamma$, a positive integer $s$ and a subgroup $G\\leq \\Aut(\\Gamma)$, we prove that $G$ is transitive on the set of $s$-arcs of $\\Gamma$ if and only if $\\Gamma$ has girth at least $2(s-1)$ and $G$ is transitive on the set of $(s-1)$-geodesics of its line graph. As applications, we first prove that the only non-complete locally cyclic $2$-geodesic transitive graphs are the complete multipartite graph $K_{3[2]}$ and the icosahedron. Secondly we classify 2-geodesic transitive graphs ...
The clique problem in ray intersection graphs
Langerman, Stefan; Cardinal, Jean; Cabello, Sergio
2015-01-01
Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph. The construction can be done in polynomial time and implies that finding a maximum clique in a segment intersection graph is NP-hard. This solves a 21-year old open problem posed by Kratochvíl and Nešetřil (Comment Math Univ Carolinae 31(1):85-93, 1990).
The Bipartite Swapping Trick on Graph Homomorphisms
Zhao, Yufei
2011-01-01
We provide an upper bound to the number of graph homomorphisms from $G$ to $H$, where $H$ is a fixed graph with certain properties, and $G$ varies over all $N$-vertex, $d$-regular graphs. This result generalizes a recently resolved conjecture of Alon and Kahn on the number of independent sets. We build on the work of Galvin and Tetali, who studied the number of graph homomorphisms from $G$ to $H$ when $H$ is bipartite. We also apply our techniques to graph colorings and stable set polytopes.
Proving relations between modular graph functions
Basu, Anirban
2016-12-01
We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non-trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links.
On Wiener index of graph complements
Directory of Open Access Journals (Sweden)
Jaisankar Senbagamalar
2014-06-01
Full Text Available Let $G$ be an $(n,m$-graph. We say that $G$ has property $(ast$ if for every pair of its adjacent vertices $x$ and $y$, there exists a vertex $z$, such that $z$ is not adjacent to either $x$ or $y$. If the graph $G$ has property $(ast$, then its complement $overline G$ is connected, has diameter 2, and its Wiener index is equal to $binom{n}{2}+m$, i.e., the Wiener index is insensitive of any other structural details of the graph $G$. We characterize numerous classes of graphs possessing property $(ast$, among which are trees, regular, and unicyclic graphs.
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar
2016-10-06
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
No finite $5$-regular matchstick graph exists
2014-01-01
A graph $G=(V,E)$ is called a unit-distance graph in the plane if there is an injective embedding of $V$ in the plane such that every pair of adjacent vertices are at unit distance apart. If additionally the corresponding edges are non-crossing and all vertices have the same degree $r$ we talk of a regular matchstick graph. Due to Euler's polyhedron formula we have $r\\le 5$. The smallest known $4$-regular matchstick graph is the so called Harborth graph consisting of $52$ vertices. In this ar...
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the joint tree model introduced by Liu, the genera of further types of graphs not necessary to have certain symmetry can be obtained. In this paper, we obtain the genus of a new type of graph with weak symmetry. As a corollary, the genus of complete tripartite graph K n,n,l (l≥n≥2) is also derived. The method used here is more direct than those methods, such as current graph, used to calculate the genus of a graph and can be realized in polynomial time.
Constrained Graph Optimization: Interdiction and Preservation Problems
Energy Technology Data Exchange (ETDEWEB)
Schild, Aaron V [Los Alamos National Laboratory
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
Generalized graph states based on Hadamard matrices
Energy Technology Data Exchange (ETDEWEB)
Cui, Shawn X. [Department of Mathematics, University of California, Santa Barbara, California 93106 (United States); Yu, Nengkun [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China); Zeng, Bei [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8 (Canada)
2015-07-15
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study the entanglement structures of these generalized graph states and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X, Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.
Constraint-Preserving Architecture Transformations: A Graph Rewriting Approach
Institute of Scientific and Technical Information of China (English)
YUAN Chun; CHEN Yiyun
2001-01-01
Architecture transformations are frequently performed during software design and maintenance. However this activity is not well supported at a sufficiently abstract level.In this paper, the authors characterize architecture transformations using graph rewriting rules,where architectures are represented in graph notations. Architectures are usually required to satisfy certain constraints during evolution. Therefore a way is presented to construct the sufficient and necessary condition for a transformation to preserve a constraint. The condition can be verified before the application of the transformation. Validated transformations are guaranteed not to violate corresponding constraints whenever applied.
MAP Estimation, Message Passing, and Perfect Graphs
Jebara, Tony S
2012-01-01
Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for singly-connected graphs and other limited settings. This article extends the set of graphs where MAP estimation is in P and where message passing recovers the exact solution to so-called perfect graphs. This result leverages recent progress in defining perfect graphs (the strong perfect graph theorem), linear programming relaxations of MAP estimation and recent convergent message passing schemes. The article converts graphical models into nand Markov random fields which are straightforward to relax into linear programs. Therein, integrality can be established in general by testing for graph perfection. This perfection test is performed efficiently using a polynomial time algorithm. Alternatively, known decomposition tools from perfect graph theory may be used to prove perfection ...
Fast approximate quadratic programming for graph matching.
Directory of Open Access Journals (Sweden)
Joshua T Vogelstein
Full Text Available Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs, we find that it efficiently achieves performance.
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.
The Feynman Identity for Planar Graphs
da Costa, G. A. T. F.
2016-08-01
The Feynman identity (FI) of a planar graph relates the Euler polynomial of the graph to an infinite product over the equivalence classes of closed nonperiodic signed cycles in the graph. The main objectives of this paper are to compute the number of equivalence classes of nonperiodic cycles of given length and sign in a planar graph and to interpret the data encoded by the FI in the context of free Lie superalgebras. This solves in the case of planar graphs a problem first raised by Sherman and sets the FI as the denominator identity of a free Lie superalgebra generated from a graph. Other results are obtained. For instance, in connection with zeta functions of graphs.
An algebraic approach to graph codes
DEFF Research Database (Denmark)
Pinero, Fernando
theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four......This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding...... are optimal or best known for their parameters. In chapter five we study some graph codes with Reed–Solomon component codes. The underlying graph is well known and widely used for its good characteristics. This helps us to compute the dimension of the graph codes. We also introduce a combinatorial concept...
Minimal regular 2-graphs and applications
Institute of Scientific and Technical Information of China (English)
FAN; Hongbing; LIU; Guizhen; LIU; Jiping
2006-01-01
A 2-graph is a hypergraph with edge sizes of at most two. A regular 2-graph is said to be minimal if it does not contain a proper regular factor. Let f2(n) be the maximum value of degrees over all minimal regular 2-graphs of n vertices. In this paper, we provide a structure property of minimal regular 2-graphs, and consequently, prove that f2(n) = n+3-i/3where 1 ≤i≤6, i=n (mod 6) andn≥ 7, which solves a conjecture posed by Fan, Liu, Wu and Wong. As applications in graph theory, we are able to characterize unfactorable regular graphs and provide the best possible factor existence theorem on degree conditions. Moreover, f2(n) and the minimal 2-graphs can be used in the universal switch box designs, which originally motivated this study.
Triangle Counting in Dynamic Graph Streams
DEFF Research Database (Denmark)
Bulteau, Laurent; Froese, Vincent; Pagh, Rasmus
2015-01-01
, with a few exceptions, the algorithms have considered insert-only streams. We present a new algorithm estimating the number of triangles in dynamic graph streams where edges can be both inserted and deleted. We show that our algorithm achieves better time and space complexity than previous solutions......Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in an arbitrary order or as incidence lists. However...... for various graph classes, for example sparse graphs with a relatively small number of triangles. Also, for graphs with constant transitivity coefficient, a common situation in real graphs, this is the first algorithm achieving constant processing time per edge. The result is achieved by a novel approach...
A kaleidoscopic view of graph colorings
Zhang, Ping
2016-01-01
This book describes kaleidoscopic topics that have developed in the area of graph colorings. Unifying current material on graph coloring, this book describes current information on vertex and edge colorings in graph theory, including harmonious colorings, majestic colorings, kaleidoscopic colorings and binomial colorings. Recently there have been a number of breakthroughs in vertex colorings that give rise to other colorings in a graph, such as graceful labelings of graphs that have been reconsidered under the language of colorings. The topics presented in this book include sample detailed proofs and illustrations, which depicts elements that are often overlooked. This book is ideal for graduate students and researchers in graph theory, as it covers a broad range of topics and makes connections between recent developments and well-known areas in graph theory.
On Second Order Degree of Graphs
Institute of Scientific and Technical Information of China (English)
Gabriela ARAUJO-PARDO; Camino BALBUENA; Mika OLSEN; Pilar VALENCIA
2012-01-01
Given a vertex v of a graph G the second order degree of v denoted as d2 (v) is defined as the number of vertices at distance 2 from v.In this paper we address the following question:What are the sufficient conditions for a graph to have a vertex v such that d2(v) ≥ d(v),where d(v) denotes the degree of v? Among other results,every graph of minimum degree exactly 2,except four graphs,is shown to have a vertex of second order degree as large as its own degree.Moreover,every K-4-free graph or every maximal planar graph is shown to have a vertex v such that d2(v) ≥ d(v).Other sufficient conditions on graphs for guaranteeing this property are also proved.
Fibonacci number of the tadpole graph
Directory of Open Access Journals (Sweden)
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Rosé, Carolyn Penstein; Ferschke, Oliver
2016-01-01
This article offers a vision for technology supported collaborative and discussion-based learning at scale. It begins with historical work in the area of tutorial dialogue systems. It traces the history of that area of the field of Artificial Intelligence in Education as it has made an impact on the field of Computer-Supported Collaborative…
Rosé, Carolyn Penstein; Ferschke, Oliver
2016-01-01
This article offers a vision for technology supported collaborative and discussion-based learning at scale. It begins with historical work in the area of tutorial dialogue systems. It traces the history of that area of the field of Artificial Intelligence in Education as it has made an impact on the field of Computer-Supported Collaborative…
Shroff, Ronnie H.; Vogel, Douglas R.
2009-01-01
Research has established that intrinsic motivation has a positive effect on learning and academic achievement. In order to investigate the phenomenon of intrinsic motivation in technology-supported learning environments, this paper investigates the factors deemed to support individual student intrinsic motivation in online discussions. A research…
Kumar, David Devraj
2017-01-01
This paper reports an analysis of an interactive technology-supported, problem-based learning (PBL) project in science, technology, engineering and mathematics (STEM) from a Learning Sciences perspective using the Selected Learning Sciences Interest Areas (SLSIA). The SLSIA was adapted from the "What kinds of topics do ISLS [International…
Line graphs as social networks
Krawczyk, M. J.; Muchnik, L.; Mańka-Krasoń, A.; Kułakowski, K.
2011-07-01
It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×10 6 people.
Baillie, C F; Johnston, D A; Plechác, P
1995-01-01
In a recent paper we found strong evidence from simulations that the Ising antiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed a mean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice, or in previous replica calculations. We then investigate numerically spin glasses with a plus or minus J bond distribution fo rthe Ising and Q=3,3,10,50 state Potts models, paying particular attention t...
A Planarity Criterion for Graphs
Dosen, Kosta
2012-01-01
It is proven that a connected graph is planar if and only if all its cocycles with at least four edges are "grounded" in the graph. The notion of grounding of this planarity criterion, which is purely combinatorial, stems from the intuitive idea that with planarity there should be a linear ordering of the edges of a cocycle such that in the two subgraphs remaining after the removal of these edges there can be no crossing of disjoint paths that join the vertices of these edges. The proof given in the paper of the right-to-left direction of the equivalence is based on Kuratowski's Theorem for planarity involving $K_{3,3}$ and $K_5$, but the criterion itself does not mention $K_{3,3}$ and $K_5$. Some other variants of the criterion are also shown necessary and sufficient for planarity.
Zhang, Ping
2015-01-01
A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings...
Line graphs as social networks
Krawczyk, Malgorzata; Mańka-Krasoń, Anna; Kułakowski, Krzysztof
2010-01-01
The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8 x 10^6 people. In particular, sharp maxima of the observed data of the degree dependence of the clustering coefficient C(k) are associated with cliques in the social network.
Graph distance for complex networks
Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki
2016-10-01
Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions.
Quantum walks on Cayley graphs
Acevedo, O L
2006-01-01
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. Thus we consider quantum walks on a general basis and try to classify them as a preliminary step in the construction of new algorithms that could be devised in this way. In particular, we discuss the choice of the dimension of the local Hilbert space, and consider various classes of graphs on which the structure of quantum walks may differ. We characterize completely the quantum walks on free groups and present partial results on more general cases. Examples are given among which a family of quantum walks on the hypercube involving a Clifford Algebra.
Waldorp, Lourens J
2016-01-01
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To analyse changes over time and characterise possible future behaviour is rather difficult for large graphs. We describe the dynamics of networks using one-dimensional discrete time dynamical systems theory obtained from a mean field approach to (elementary) probabilistic cellular automata (PCA). Often the mean field approach is used on a regular graph (a grid or torus) where each node has the same number of edges and the same probability of becoming active. We show that we can use variations of the mean field of the grid to describe the dynamics of the PCA on a random and small-world graph. Bifurcation diagrams for the mean field of the grid, random, and small-world graphs indicate possible phase transitions for certain parameter settings. Extensive simulations indicate for di...
Decomposing a graph into bistars
DEFF Research Database (Denmark)
Thomassen, Carsten
2013-01-01
Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which...
2015-01-01
In this paper we develop a formal dynamic version of Chain Event Graphs (CEGs), a particularly expressive family of discrete graphical models. We demonstrate how this class links to semi-Markov models and provides a convenient generalization of the Dynamic Bayesian Network (DBN). In particular we develop a repeating time-slice Dynamic CEG providing a useful and simpler model in this family. We demonstrate how the Dynamic CEG’s graphical formulation exhibits asymmetric conditional independence...
Matrix Completions and Chordal Graphs
Institute of Scientific and Technical Information of China (English)
Kenneth John HARRISON
2003-01-01
In a matrix-completion problem the aim is to specifiy the missing entries of a matrix inorder to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where we look for completions of various types for partial matrices supported ona given pattern. We see that thc existence of completions of the required type often depends on thechordal properties of graphs associated with the pattern.
Parallel External Memory Graph Algorithms
DEFF Research Database (Denmark)
Arge, Lars Allan; Goodrich, Michael T.; Sitchinava, Nodari
2010-01-01
In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one o f the private-cache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to efficient solutions to problems on trees, such as computing lowest...... an optimal speedup of Â¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....
Dynamic molecular graphs: "hopping" structures.
Cortés-Guzmán, Fernando; Rocha-Rinza, Tomas; Guevara-Vela, José Manuel; Cuevas, Gabriel; Gómez, Rosa María
2014-05-05
This work aims to contribute to the discussion about the suitability of bond paths and bond-critical points as indicators of chemical bonding defined within the theoretical framework of the quantum theory of atoms in molecules. For this purpose, we consider the temporal evolution of the molecular structure of [Fe{C(CH2 )3 }(CO)3 ] throughout Born-Oppenheimer molecular dynamics (BOMD), which illustrates the changing behaviour of the molecular graph (MG) of an electronic system. Several MGs with significant lifespans are observed across the BOMD simulations. The bond paths between the trimethylenemethane and the metallic core are uninterruptedly formed and broken. This situation is reminiscent of a "hopping" ligand over the iron atom. The molecular graph wherein the bonding between trimethylenemethane and the iron atom takes place only by means of the tertiary carbon atom has the longest lifespan of all the considered structures, which is consistent with the MG found by X-ray diffraction experiments and quantum chemical calculations. In contrast, the η(4) complex predicted by molecular-orbital theory has an extremely brief lifetime. The lifespan of different molecular structures is related to bond descriptors on the basis of the topology of the electron density such as the ellipticities at the FeCH2 bond-critical points and electron delocalisation indices. This work also proposes the concept of a dynamic molecular graph composed of the different structures found throughout the BOMD trajectories in analogy to a resonance hybrid of Lewis structures. It is our hope that the notion of dynamic molecular graphs will prove useful in the discussion of electronic systems, in particular for those in which analysis on the basis of static structures leads to controversial conclusions. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
On Making Directed Graphs Eulerian
Sorge, Manuel
2011-01-01
A directed graph is called Eulerian, if it contains a walk that traverses every arc in the graph exactly once. We study the problem of Eulerian Extension (EE) where a directed multigraph G and a weight function is given and it is asked whether G can be made Eulerian by adding arcs whose total weight does not exceed a given threshold. This problem is motivated through applications in vehicle routing and flowshop scheduling. However, EE is NP- hard and thus we use the parameterized complexity framework to analyze it. In parameterized complexity, the running time of algorithms is considered not only with respect to input length, but also with respect to other properties of the input-called "parameters". Dorn et al. proved that EE can be solved in O(4^k n^4) time, where k denotes the parameter "number of arcs that have to be added". In this thesis, we analyze EE with respect to the (smaller) parameters "number c of connected components in the input graph" and "sum b over indeg(v) - outdeg(v) for all vertices v in...
Restrained roman domination in graphs
Directory of Open Access Journals (Sweden)
Roushini Leely Pushpam
2015-03-01
Full Text Available A Roman dominating function (RDF on a graph G = (V,E is defined to be a function satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. A set S V is a Restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in . We define a Restrained Roman dominating function on a graph G = (V,E to be a function satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2 and at least one vertex w for which f(w = 0. The weight of a Restrained Roman dominating function is the value . The minimum weight of a Restrained Roman dominating function on a graph G is called the Restrained Roman domination number of G and denoted by . In this paper, we initiate a study of this parameter.
Metabolic networks: beyond the graph.
Bernal, Andrés; Daza, Edgar
2011-06-01
Drugs are devised to enter into the metabolism of an organism in order to produce a desired effect. From the chemical point of view, cellular metabolism is constituted by a complex network of reactions transforming metabolites one in each other. Knowledge on the structure of this network could help to develop novel methods for drug design, and to comprehend the root of known unexpected side effects. Many large-scale studies on the structure of metabolic networks have been developed following models based on different kinds of graphs as the fundamental image of the reaction network. Graphs models, however, comport wrong assumptions regarding the structure of reaction networks that may lead into wrong conclusions if they are not taken into account. In this article we critically review some graph-theoretical approaches to the analysis of centrality, vulnerability and modularity of metabolic networks, analyzing their limitations in estimating these key network properties, consider some proposals explicit or implicitly based on directed hypergraphs regarding their ability to overcome these issues, and review some recent implementation improvements that make the application of these models in increasingly large networks a viable option.
Sparse graphs are not flammable
Prałat, Paweł
2012-01-01
In this paper, we consider the following \\emph{$k$-many firefighter problem} on a finite graph $G=(V,E)$. Suppose that a fire breaks out at a given vertex $v \\in V$. In each subsequent time unit, a firefighter protects $k$ vertices which are not yet on fire, and then the fire spreads to all unprotected neighbours of the vertices on fire. The objective of the firefighter is to save as many vertices as possible. The surviving rate $\\rho(G)$ of $G$ is defined as the expected percentage of vertices that can be saved when a fire breaks out at a random vertex of $G$. Let $\\tau_k = k+2-\\frac {1}{k+2}$. We show that for any $\\eps >0$ and $k \\ge 2$, each graph $G$ on $n$ vertices with at most $(\\tau_k-\\eps)n$ edges is not flammable; that is, $\\rho(G) > \\frac {2\\eps}{5\\tau_k} > 0$. Moreover, a construction of a family of flammable random graphs is proposed to show that the constant $\\tau_k$ cannot be improved.
Topological structure of dictionary graphs
Fukś, Henryk; Krzemiński, Mark
2009-09-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Dynkin graphs and quadrilateral singularities
Urabe, Tohsuke
1993-01-01
The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs wil...
On Self-Centeredness of Product of Graphs
Directory of Open Access Journals (Sweden)
Priyanka Singh
2016-01-01
Full Text Available A graph G is said to be a self-centered graph if the eccentricity of every vertex of the graph is the same. In other words, a graph is a self-centered graph if radius and diameter of the graph are equal. In this paper, self-centeredness of strong product, co-normal product, and lexicographic product of graphs is studied in detail. The necessary and sufficient conditions for these products of graphs to be a self-centered graph are also discussed. The distance between any two vertices in the co-normal product of a finite number of graphs is also computed analytically.
Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph
Directory of Open Access Journals (Sweden)
P. Anusha Devi
2015-10-01
Full Text Available An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G,$ is the minimum number of da-ecards that uniquely determines $G.$ The adversary degree associated edge reconstruction number of a graph $G, adern(G,$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs.
Indexing molecules with chemical graph identifiers.
Gregori-Puigjané, Elisabet; Garriga-Sust, Rut; Mestres, Jordi
2011-09-01
Fast and robust algorithms for indexing molecules have been historically considered strategic tools for the management and storage of large chemical libraries. This work introduces a modified and further extended version of the molecular equivalence number naming adaptation of the Morgan algorithm (J Chem Inf Comput Sci 2001, 41, 181-185) for the generation of a chemical graph identifier (CGI). This new version corrects for the collisions recognized in the original adaptation and includes the ability to deal with graph canonicalization, ensembles (salts), and isomerism (tautomerism, regioisomerism, optical isomerism, and geometrical isomerism) in a flexible manner. Validation of the current CGI implementation was performed on the open NCI database and the drug-like subset of the ZINC database containing 260,071 and 5,348,089 structures, respectively. The results were compared with those obtained with some of the most widely used indexing codes, such as the CACTVS hash code and the new InChIKey. The analyses emphasize the fact that compound management activities, like duplicate analysis of chemical libraries, are sensitive to the exact definition of compound uniqueness and thus still depend, to a minor extent, on the type and flexibility of the molecular index being used.
Finding Light Spanners in Bounded Pathwidth Graphs
Grigni, Michelangelo
2011-01-01
Given an edge-weighted graph $G$ and $\\epsilon>0$, a $(1+\\epsilon)$-spanner is a spanning subgraph $G'$ whose shortest path distances approximate those of $G$ within a $(1+\\epsilon)$ factor. If $G$ is from certain minor-closed graph families (at least bounded genus graphs and apex graphs), then we know that light spanners exist. That is, we can compute a $(1+\\epsilon)$-spanner $G'$ with total edge weight at most a constant times the weight of a minimum spanning tree. This constant may depend on $\\epsilon$ and the graph family, but not on the particular graph $G$ nor on its edge weighting. For weighted graphs from several minor-closed graph families, the existence of light spanners has been essential in the design of approximation schemes for the metric TSP (the traveling salesman problem) and some similar problems. In this paper we make some progress towards the conjecture that light spanners exist for every minor-closed graph family. In particular, we show that they exist for graphs with bounded pathwidth. W...
Minimum degree condition forcing complete graph immersion
DeVos, Matt; Fox, Jacob; McDonald, Jessica; Mohar, Bojan; Scheide, Diego
2011-01-01
An immersion of a graph $H$ into a graph $G$ is a one-to-one mapping $f:V(H) \\to V(G)$ and a collection of edge-disjoint paths in $G$, one for each edge of $H$, such that the path $P_{uv}$ corresponding to edge $uv$ has endpoints $f(u)$ and $f(v)$. The immersion is strong if the paths $P_{uv}$ are internally disjoint from $f(V(H))$. It is proved that for every positive integer $t$, every simple graph of minimum degree at least $200t$ contains a strong immersion of the complete graph $K_t$. For dense graphs one can say even more. If the graph has order $n$ and has $2cn^2$ edges, then there is a strong immersion of the complete graph on at least $c^2 n$ vertices in $G$ in which each path $P_{uv}$ is of length 2. As an application of these results, we resolve a problem raised by Paul Seymour by proving that the line graph of every simple graph with average degree $d$ has a clique minor of order at least $cd^{3/2}$, where $c>0$ is an absolute constant. For small values of $t$, $1\\le t\\le 7$, every simple graph of...
Inferring Pedigree Graphs from Genetic Distances
Tamura, Takeyuki; Ito, Hiro
In this paper, we study a problem of inferring blood relationships which satisfy a given matrix of genetic distances between all pairs of n nodes. Blood relationships are represented by our proposed graph class, which is called a pedigree graph. A pedigree graph is a directed acyclic graph in which the maximum indegree is at most two. We show that the number of pedigree graphs which satisfy the condition of given genetic distances may be exponential, but they can be represented by one directed acyclic graph with n nodes. Moreover, an O(n3) time algorithm which solves the problem is also given. Although phylogenetic trees and phylogenetic networks are similar data structures to pedigree graphs, it seems that inferring methods for phylogenetic trees and networks cannot be applied to infer pedigree graphs since nodes of phylogenetic trees and networks represent species whereas nodes of pedigree graphs represent individuals. We also show an O(n2) time algorithm which detects a contradiction between a given pedigreee graph and distance matrix of genetic distances.
Institute of Scientific and Technical Information of China (English)
魏二玲; 刘颜佩
2004-01-01
For a graph G of size ε≥1 and its edge-induced subgraphs H1 and H2 of size γ(1 < γ < ε), H1 is said to be obtained from H2 by an edge jump if there exist four distinct vertices u, v, ω and x in G such that (u,v)∈E(H2), (ω,x)∈E(G) - E(H2) and H1=H2 - (u, v) + (ω, x). In this article, the γ-jump graphs(r≥3) are discussed. A graph H is said to be an γ-jump graph of G if its vertices correspond to the edge induced graph of size γ in G and two vertices are adjacent if and only if one of the two corresponding subgraphs can be obtained from the other by an edge jump. For k≥2, the k-th iterated γ-jump graph Jrk(G) is defined as Jγ(Jγk-1 (G)), where Jγ1 (G) = Jγ(G). An infinite sequence {Gi} of graphs is planar if every graph Gi is planar. It is shown that there does not exist a graph G for which the sequence {J3k(G)} is planar, where k is any positive integer. Meanwhile, lim gen(J3k(G)) =∞, where gen(G) denotes the genus of a graph G, if the sequence k→∞J3k(G) is defined for every positive integer k. As for the 4-jump graph of a graph G,{J4k(G)} is planar if and only if G = C5. For γ≥5, whether the fix graph of the sequence {Jγk(G))exists is determined.
Graphs whose Complement and Square are Isomorphic (extended version)
DEFF Research Database (Denmark)
Pedersen, Anders Sune; Milanic, Martin; Verret, Gabriel
2013-01-01
We study square-complementary graphs, that is, graphs whose comple- ment and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct innite families of square......-complementary graphs, and characterize square-complementary graphs within various graph classes. The bipartite case turns out to be of particular interest....
Generalized Graphs, Methods for Obtaining Graph Spectra. Application of Graph Spectra in Chemistry
Shen, Mingzuo
Various graphical methods in the literature for getting at some features of the MO energy level spectra of especially pi systems and some related three-dimensional molecules are studied in detail. These include the graphical methods of Sinanoglu (although its mathematical, quantum-physical foundations, e.g. Sinanoglu's structural-covariance theory, are not discussed in this thesis), the edge-deletion method of Jiang, the specialized method of Sheng for benzenoid graphs, pairing theorems, graph splitting methods of e.g. McClelland, and more general one of R. A. Davidson. Of these the Sinanoglu method is found to be the only one generally applicable to diverse types of molecules without the need to introduce additional and complicated rules for each new graph type. The Sinanoglu method however is intended to be only a qualitative tool (giving the number of bonding, nonbonding, and antibonding levels and their changes upon reaction or geometrical distortions, large or small, of the molecule). Thus the other methods, although highly specialized, could be of help in getting some further information on the spectra. In particular, the "negative graph" concept in Chapter 3 of this thesis would be found useful in ascertaining the energy gap between the lowest and highest MO levels. In case where the Sinanoglu method cannot distinguish between differing stabilities of two molecules with the same signature and number of elections, this energy gap will be particularly useful. In the thesis, many alternative and simpler derivations of the graph-theoretic methods of Jiang, Davidson and others mentioned above are given. Some methods are generalized further. In the last chapter of the thesis starting with S 5.3, the graphical method is applied extensively to various types of molecules thought to have through-space interactions. Especially the Sinanoglu method is used to obtain the signature (instead of using a computer) and qualitative stabilities of these molecules are discussed
Roman Bondage Numbers of Some Graphs
Hu, Fu-Tao
2011-01-01
A Roman dominating function on a graph $G=(V,E)$ is a function $f: V\\to \\{0,1,2\\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The weight of a Roman dominating function is the value $f(G)=\\sum_{u\\in V} f(u)$. The Roman domination number of $G$ is the minimum weight of a Roman dominating function on $G$. The Roman bondage number of a nonempty graph $G$ is the minimum number of edges whose removal results in a graph with the Roman domination number larger than that of $G$. This paper determines the exact value of the Roman bondage numbers of two classes of graphs, complete $t$-partite graphs and $(n-3)$-regular graphs with order $n$ for any $n\\ge 5$.
Term Graph Rewriting and Parallel Term Rewriting
Corradini, Andrea; 10.4204/EPTCS.48.3
2011-01-01
The relationship between Term Graph Rewriting and Term Rewriting is well understood: a single term graph reduction may correspond to several term reductions, due to sharing. It is also known that if term graphs are allowed to contain cycles, then one term graph reduction may correspond to infinitely many term reductions. We stress that this fact can be interpreted in two ways. According to the "sequential interpretation", a term graph reduction corresponds to an infinite sequence of term reductions, as formalized by Kennaway et.al. using strongly converging derivations over the complete metric space of infinite terms. Instead according to the "parallel interpretation" a term graph reduction corresponds to the parallel reduction of an infinite set of redexes in a rational term. We formalize the latter notion by exploiting the complete partial order of infinite and possibly partial terms, and we stress that this interpretation allows to explain the result of reducing circular redexes in several approaches to te...
Aspects of randomness in neural graph structures
Rudolph-Lilith, Michelle
2013-01-01
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural systems, however, a few moderately robust experimental reconstructions do exist, and these have long served as fundamental prototypes for studying connectivity patterns in the nervous system. In this paper, we provide a comparative analysis of these "historical" graphs, both in (unmodified) directed and (often symmetrized) undirected forms, and focus on simple structural characterizations of their connectivity. We find that in most measures the networks studied are captured by simple random graph models; in a few key measures, however, we observe a marked departure from the random graph prediction. Our results suggest that the mechanism of graph formation in th...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2011-01-01
We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics, which we refocus into the first storeless abstract machine...... for combinatory graph reduction, which we refunctionalize into the first storeless natural semantics for combinatory graph reduction.We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one...... of term graphs in the sense of Barendregt et al. The corresponding storeless abstract machine and natural semantics follow mutatis mutandis. We then interpret let expressions as operations over a global store (thus shifting, in Strachey's words, from denotable entities to storable entities), resulting...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2013-01-01
We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this rst syntactic theory as a storeless reduction semantics of combinatory terms. We then factor out...... the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand . The factored terms can be interpreted as term graphs in the sense of Barendregt et al. We express this second syntactic theory, which we prove equivalent to the rst, as a storeless reduction semantics...... of combinatory term graphs. We then recast let bindings as bindings in a global store, thus shifting, in Strachey's words, from denotable entities to storable entities. The store-based terms can still be interpreted as term graphs. We express this third syntactic theory, which we prove equivalent to the second...
Complexity Results on Graphs with Few Cliques
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Bill Rosgen
2007-01-01
Full Text Available A graph class has few cliques if there is a polynomial bound on the number of maximal cliques contained in any member of the class. This restriction is equivalent to the requirement that any graph in the class has a polynomial sized intersection representation that satisfies the Helly property. On any such class of graphs, some problems that are NP-complete on general graphs, such as the maximum clique problem and the maximum weighted clique problem, admit polynomial time algorithms. Other problems, such as the vertex clique cover and edge clique cover problems remain NP-complete on these classes. Several classes of graphs which have few cliques are discussed, and the complexity of some partitioning and covering problems are determined for the class of all graphs which have fewer cliques than a given polynomial bound.
Search Algorithms for Conceptual Graph Databases
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Abdurashid Mamadolimov
2013-03-01
Full Text Available We consider a database composed of a set of conceptual graphs. Using conceptual graphs and graphhomomorphism it is possible to build a basic query-answering mechanism based on semantic search.Graph homomorphism defines a partial order over conceptual graphs. Since graph homomorphismchecking is an NP-Complete problem, the main requirement for database organizing and managingalgorithms is to reduce the number of homomorphism checks. Searching is a basic operation for databasemanipulating problems. We consider the problem of searching for an element in a partially ordered set.The goal is to minimize the number of queries required to find a target element in the worst case. First weanalyse conceptual graph database operations. Then we propose a new algorithm for a subclass of lattices.Finally, we suggest a parallel search algorithm for a general poset.
Notes on large angle crossing graphs
Dujmovic, Vida; Morin, Pat; Wolle, Thomas
2009-01-01
A graph G is an a-angle crossing (aAC) graph if every pair of crossing edges in G intersect at an angle of at least a. The concept of right angle crossing (RAC) graphs (a=Pi/2) was recently introduced by Didimo et. al. It was shown that any RAC graph with n vertices has at most 4n-10 edges and that there are infinitely many values of n for which there exists a RAC graph with n vertices and 4n-10 edges. In this paper, we give upper and lower bounds for the number of edges in aAC graphs for all 0 < a < Pi/2.
Determinants of adjacency matrices of graphs
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Alireza Abdollahi
2012-12-01
Full Text Available We study the set of all determinants of adjacency matrices of graphs with a given number of vertices. Using Brendan McKay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. Using an idea of M. Newman, it is proved that if $G$ is a graph with $n$ vertices and ${d_1,dots,d_n}$ is the set of vertex degrees of $G$, then $gcd(2m,d^2$ divides the determinant of the adjacency matrix of $G$, where $d=gcd(d_1,dots,d_n$. Possible determinants of adjacency matrices of graphs with exactly two cycles are obtained.
Malware Classification based on Call Graph Clustering
Kinable, Joris
2010-01-01
Each day, anti-virus companies receive tens of thousands samples of potentially harmful executables. Many of the malicious samples are variations of previously encountered malware, created by their authors to evade pattern-based detection. Dealing with these large amounts of data requires robust, automatic detection approaches. This paper studies malware classification based on call graph clustering. By representing malware samples as call graphs, it is possible to abstract certain variations away, and enable the detection of structural similarities between samples. The ability to cluster similar samples together will make more generic detection techniques possible, thereby targeting the commonalities of the samples within a cluster. To compare call graphs mutually, we compute pairwise graph similarity scores via graph matchings which approximately minimize the graph edit distance. Next, to facilitate the discovery of similar malware samples, we employ several clustering algorithms, including k-medoids and DB...
Graphs in machine learning: an introduction
Latouche, Pierre
2015-01-01
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper, we give an introduction to some methods relying on graphs for learning. This includes both unsupervised and supervised methods. Unsupervised learning algorithms usually aim at visualising graphs in latent spaces and/or clustering the nodes. Both focus on extracting knowledge from graph topologies. While most existing techniques are only applicable to static graphs, where edges do not evolve through time, recent developments have shown that they could be extended to deal with evolving networks. In a supervised context, one generally aims at inferring labels or numerical values attached to nodes using both the graph and, when they are available, node characteristics. Balancing the two sources of information can be challenging, especially as they can disagree locally or globall...
LGM: Mining Frequent Subgraphs from Linear Graphs
Tabei, Yasuo; Hirose, Shuichi; Tsuda, Koji
2011-01-01
A linear graph is a graph whose vertices are totally ordered. Biological and linguistic sequences with interactions among symbols are naturally represented as linear graphs. Examples include protein contact maps, RNA secondary structures and predicate-argument structures. Our algorithm, linear graph miner (LGM), leverages the vertex order for efficient enumeration of frequent subgraphs. Based on the reverse search principle, the pattern space is systematically traversed without expensive duplication checking. Disconnected subgraph patterns are particularly important in linear graphs due to their sequential nature. Unlike conventional graph mining algorithms detecting connected patterns only, LGM can detect disconnected patterns as well. The utility and efficiency of LGM are demonstrated in experiments on protein contact maps.
Parallel Graph Partitioning for Complex Networks
Meyerhenke, Henning; Schulz, Christian
2014-01-01
Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel graph partitioners originally developed for more regular mesh-like networks do not work well for these networks. This paper addresses this problem by parallelizing and adapting the label propagation technique originally developed for graph clustering. By introducing size constraints, label propagation becomes applicable for both the coarsening and the refinement phase of multilevel graph partitioning. We obtain very high quality by applying a highly parallel evolutionary algorithm to the coarsened graph. The resulting system is both more scalable and achieves higher quality than state-of-the-art systems like ParMetis or PT-Scotch. For large complex networks the performance differences are very big. For example, our algorithm can partition a web graph with 3.3 billion edges ...
Efficient Snapshot Retrieval over Historical Graph Data
Khurana, Udayan
2012-01-01
We address the problem of managing historical data for large evolving information networks like social networks or citation networks, with the goal to enable temporal and evolutionary queries and analysis. We present the design and architecture of a distributed graph database system that stores the entire history of a network and provides support for efficient retrieval of multiple graphs from arbitrary time points in the past, in addition to maintaining the current state for ongoing updates. Our system exposes a general programmatic API to process and analyze the retrieved snapshots. We introduce DeltaGraph, a novel, extensible, highly tunable, and distributed hierarchical index structure that enables compactly recording the historical information, and that supports efficient retrieval of historical graph snapshots for single-site or parallel processing. Along with the original graph data, DeltaGraph can also maintain and index auxiliary information; this functionality can be used to extend the structure to ...
The Dynamics of the Forest Graph Operator
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Dara Suresh
2016-11-01
Full Text Available In 1966, Cummins introduced the “tree graph”: the tree graph T(G of a graph G (possibly infinite has all its spanning trees as vertices, and distinct such trees correspond to adjacent vertices if they differ in just one edge, i.e., two spanning trees T1 and T2 are adjacent if T2 = T1 − e + f for some edges e ∈ T1 and f ∉ T1. The tree graph of a connected graph need not be connected. To obviate this difficulty we define the “forest graph”: let G be a labeled graph of order α, finite or infinite, and let N(G be the set of all labeled maximal forests of G. The forest graph of G, denoted by F(G, is the graph with vertex set N(G in which two maximal forests F1, F2 of G form an edge if and only if they differ exactly by one edge, i.e., F2 = F1 − e + f for some edges e ∈ F1 and f ∉ F1. Using the theory of cardinal numbers, Zorn’s lemma, transfinite induction, the axiom of choice and the well-ordering principle, we determine the F-convergence, F-divergence, F-depth and F-stability of any graph G. In particular it is shown that a graph G (finite or infinite is F-convergent if and only if G has at most one cycle of length 3. The F-stable graphs are precisely K3 and K1. The F-depth of any graph G different from K3 and K1 is finite. We also determine various parameters of F(G for an infinite graph G, including the number, order, size, and degree of its components.
Graph Zeta function and gauge theories
He, Yang-Hui
2011-03-01
Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of quiver theories and periodic tilings by bi-partite graphs. In particular, we examine issues such as the spectra of the adjacency and whether the gauge theory satisfies the strong and weak versions of the graph theoretical analogue of the Riemann Hypothesis.