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Graph Polynomials (Discrete Mathematics and Its Applications)
by Yongtang Shi; Matthias Dehmer; Xueliang Li; Ivan GutmanThis book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.
Graph Sampling
by Li-Chun ZhangMany technological, socio-economic, environmental, biomedical phenomena exhibit an underlying graph structure. Valued graph allows one to incorporate the connections or links among the population units in addition. The links may provide effectively access to the part of population that is the primary target, which is the case for many unconventional sampling methods, such as indirect, network, line-intercept or adaptive cluster sampling. Or, one may be interested in the structure of the connections, in terms of the corresponding graph properties or parameters, such as when various breadth- or depth-first non-exhaustive search algorithms are applied to obtain compressed views of large often dynamic graphs. Graph sampling provides a statistical approach to study real graphs from either of these perspectives. It is based on exploring the variation over all possible sample graphs (or subgraphs) which can be taken from the given population graph, by means of the relevant known sampling probabilities. The resulting design-based inference is valid whatever the unknown properties of the given real graphs. One-of-a-kind treatise of multidisciplinary topics relevant to statistics, mathematics and data science. Probabilistic treatment of breadth-first and depth-first non-exhaustive search algorithms in graphs. Presenting cutting-edge theory and methods based on latest research. Pathfinding for future research on sampling from real graphs. Graph Sampling can primarily be used as a resource for researchers working with sampling or graph problems, and as the basis of an advanced course for post-graduate students in statistics, mathematics and data science.
Graph Spectra for Complex Networks
by Piet Van MieghemAnalyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.
Graph Structure and Monadic Second-Order Logic
by Bruno Courcelle Joost EngelfrietThe study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
Graph Structures for Knowledge Representation and Reasoning: 6th International Workshop, GKR 2020, Virtual Event, September 5, 2020, Revised Selected Papers (Lecture Notes in Computer Science #12640)
by Madalina Croitoru Pierre Marquis Sebastian Rudolph Michael CochezThis open access book constitutes the thoroughly refereed post-conference proceedings of the 6th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2020, held virtually in September 2020, associated with ECAI 2020, the 24th European Conference on Artificial Intelligence.The 7 revised full papers presented together with 2 invited contributions were reviewed and selected from 9 submissions. The contributions address various issues for knowledge representation and reasoning and the common graph-theoretic background, which allows to bridge the gap between the different communities.
Graph Theoretic Methods in Multiagent Networks (Princeton Series in Applied Mathematics #33)
by Mehran Mesbahi Magnus EgerstedtThis accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? University of Stuttgart, Germany Royal Institute of Technology, Sweden Johannes Kepler University, Austria Georgia Tech, USA University of Washington, USA Ohio University, USA
Graph Theory
by Ralucca Gera Stephen Hedetniemi Craig LarsonThis is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors' favorite conjectures and open problems, enhancing the reader's overall comprehension and enthusiasm. The editors were inspired to create these volumes by the popular and well attended special sessions, entitled "My Favorite Graph Theory Conjectures," which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In an effort to aid in the creation and dissemination of open problems, which is crucial to the growth and development of a field, the editors requested the speakers, as well as notable experts in graph theory, to contribute to these volumes.
Graph Theory
by Ronald GouldThis 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. Subsequent chapters explore cycles and circuits, planarity, matchings, and independence. The text concludes with considerations of special topics and applications and extremal theory. Exercises appear throughout the text.
Graph Theory Applications to Deregulated Power Systems (SpringerBriefs in Electrical and Computer Engineering)
by Ricardo Moreno Chuquen Harold R. ChamorroThis book provides a detailed description of network science concepts applied to power systems and electricity markets, offering an appropriate blend of theoretical background and practical applications for operation and power system planning. It discusses an approach to understanding power systems from a network science perspective using the direct recognition of the interconnectivity provided by the transmission system. Further, it explores the network properties in detail and characterizes them as a tool for online and offline applications for power system operation. The book includes an in-depth explanation of electricity markets problems that can be addressed from a graph theory perspective. It is intended for advanced undergraduate and graduate students in the fields of electric energy systems, operations research, management science and economics. Practitioners in the electric energy sector also benefit from the concepts and techniques presented here.
Graph Theory and Decomposition
by Joseph Varghese Kureethara Jomon Kottarathil Sudev NaduvathThe book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems.Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory.
Graph Theory and Interconnection Networks
by Lih-Hsing Hsu Cheng-Kuan LinThe 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 gra
Graph Theory and Its Applications (Textbooks in Mathematics)
by Mark Anderson Jonathan L. Gross Jay YellenGraph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authors’ unparalleled treatment is an ideal text for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology. Features of the Third Edition Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions) Provides better coverage of algorithms and algebraic and topological graph theory than any other text Incorporates several levels of carefully designed exercises that promote student retention and develop and sharpen problem-solving skills Includes supplementary exercises to develop problem-solving skills, solutions and hints, and a detailed appendix, which reviews the textbook’s topics About the Authors Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory. Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms. Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.
Graph Theory with Algorithms and its Applications
by Santanu Saha RayThe book has many important features which make it suitable for both undergraduate and postgraduate students in various branches of engineering and general and applied sciences. The important topics interrelating Mathematics & Computer Science are also covered briefly. The book is useful to readers with a wide range of backgrounds including Mathematics, Computer Science/Computer Applications and Operational Research. While dealing with theorems and algorithms, emphasis is laid on constructions which consist of formal proofs, examples with applications. Uptill, there is scarcity of books in the open literature which cover all the things including most importantly various algorithms and applications with examples.
Graph Theory with Applications to Engineering and Computer Science
by Narsingh DeoThis outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra. Topics include paths and circuits, trees and fundamental circuits, planar and dual graphs, vector and matrix representation of graphs, and related subjects.The remaining six chapters are more advanced, covering graph theory algorithms and computer programs, graphs in switching and coding theory, electrical network analysis by graph theory, graph theory in operations research, and more. Instructors may combine these chapters with the preceding material for courses in a variety of fields, including electrical engineering, computer science, operations research, and applied mathematics.
Graph Theory: An Interactive View (Dover Books on Mathematics #61)
by Frank HararyAn effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.
Graph Theory: An Introduction to Proofs, Algorithms, and Applications (Textbooks in Mathematics)
by Karin R SaoubGraph Theory: An Introduction to Proofs, Algorithms, and Applications Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis. This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results. Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations. Current applications and exploratory exercises are provided to further the reader’s mathematical reasoning and understanding of the relevance of graph theory to the modern world. Features The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths. The third chapter focuses entirely on trees – terminology, applications, and theory. Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach. Hints and Solutions to selected exercises provided at the back of the book. Author Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She earned her PhD in mathematics from Arizona State University and BA from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.
Graph Theory: Favorite Conjectures And Open Problems - 1 (Problem Books in Mathematics)
by Ralucca Gera Teresa W. Haynes Stephen T. HedetniemiThis second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory. It is designed for both graduate students and established researchers in discrete mathematics who are searching for research ideas and references. Each chapter provides more than a simple collection of results on a particular topic; it captures the reader’s interest with techniques that worked and failed in attempting to solve particular conjectures. The history and origins of specific conjectures and the methods of researching them are also included throughout this volume. Students and researchers can discover how the conjectures have evolved and the various approaches that have been used in an attempt to solve them. An annotated glossary of nearly 300 graph theory parameters, 70 conjectures, and over 600 references is also included in this volume. This glossary provides an understanding of parameters beyond their definitions and enables readers to discover new ideas and new definitions in graph theory. The editors were inspired to create this series of volumes by the popular and well-attended special sessions entitled “My Favorite Graph Theory Conjectures,” which they organized at past AMS meetings. These sessions were held at the winter AMS/MAA Joint Meeting in Boston, January 2012, the SIAM Conference on Discrete Mathematics in Halifax in June 2012, as well as the winter AMS/MAA Joint Meeting in Baltimore in January 2014, at which many of the best-known graph theorists spoke. In an effort to aid in the creation and dissemination of conjectures and open problems, which is crucial to the growth and development of this field, the editors invited these speakers, as well as other experts in graph theory, to contribute to this series.
Graph Transformation: 11th International Conference, ICGT 2018, Held as Part of STAF 2018, Toulouse, France, June 25–26, 2018, Proceedings (Lecture Notes in Computer Science #10887)
by Leen Lambers Jens WeberThis book constitutes the refereed proceedings of the 11th International Conference on Graph Transformation, ICGT 2018, held as part of STAF 2018, in Toulouse, France, in June 2018.The 9 full papers, 2 short papers and 1 keynote presented in this book were carefully reviewed and selected from 16 submissions. The papers deal with the following topics: graph languages; graph transformation formalisms; parallel independence and conflicts; and graph conditions and verification.
Graph Transformation: 17th International Conference, ICGT 2024, Held as Part of STAF 2024, Enschede, The Netherlands, July 10–11, 2024, Proceedings (Lecture Notes in Computer Science #14774)
by Russ Harmer Jens KosiolThis book constitutes the refereed proceedings of the 17th International Conference on Graph Transformation, ICGT 2024, held in Enschede, The Netherlands, during July 10–11, 2024. The 10 full papers and 3 short papers included in this book were carefully reviewed and selected from 21 submissions. They were organized in topical sections as follows: Theoretical Advances; Application Domains; and Tool and Blue Skies Presentations.
Graph Vision: Digital Architecture’s Skeletons
by Theodora VardouliHow a protean mathematical object, the graph, ushered in new images, tools, and infrastructures for design and catalyzed a digital future for architecture.In Graph Vision, Theodora Vardouli offers a fresh history of architecture&’s early entanglements with modern mathematics and digital computing by focusing on a hidden protagonist: the graph. Fueled by iconoclastic sentiments and skepticism of geometric depiction, architects, she explains, turned to the skeletal underpinnings of their work, and with it the graph, as a site of representation, operation, and political possibility. Taking the reader on an enthralling journey through a polyvalent mathematical entity, Vardouli combines close readings of graphs&’ architectural manifestations as images, tools, and infrastructures for design with original archival work on research centers that spearheaded mathematical and computational approaches to architecture.Structured thematically, Graph Vision weaves together archival findings on influential research groups such as the Land Use Built Form Studies Center at the University of Cambridge, the Center for Environmental Structure at Berkeley, the Architecture Machine Group at the Massachusetts Institute of Technology, among others, as well as important figures who led, or worked in proximity to, these groups, including Lionel March, Christopher Alexander, and Yona Friedman. Together, this material chronicles the emergence of both a new way of seeing and a new prospect for the discipline that prefigured its digital future—of a &“graph vision.&” Vardouli argues that this vision was one of vacillation toward visual appearance. Digital approaches to architecture, she ultimately reveals, were founded on a profound ambivalence toward the visual realm endemic to mid-twentieth century architectural and mathematical modernisms.
Graph-Based Clustering and Data Visualization Algorithms
by János Abonyi Ágnes Vathy-FogarassyThis work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on the synergistic combination of clustering, graph-theory, neural networks, data visualization, dimensionality reduction, fuzzy methods, and topology learning. The work contains numerous examples to aid in the understanding and implementation of the proposed algorithms, supported by a MATLAB toolbox available at an associated website.
Graph-Based Modelling in Science, Technology and Art (Mechanisms and Machine Science #107)
by Stanisław Zawiślak Jacek RysińskiThis book presents interdisciplinary, cutting-edge and creative applications of graph theory and modeling in science, technology, architecture and art. Topics are divided into three parts: the first one examines mechanical problems related to gears, planetary gears and engineering installations; the second one explores graph-based methods applied to medical analyses as well as biological and chemical modeling; and the third part includes various topics e.g. drama analysis, aiding of design activities and network visualisation. The authors represent several countries in Europe and America, and their contributions show how different, useful and fruitful the utilization of graphs in modelling of engineering systems can be. The book has been designed to serve readers interested in the subject of graph modelling and those with expertise in related areas, as well as members of the worldwide community of graph modelers.
Graph-Based Representation and Reasoning: 24th International Conference on Conceptual Structures, ICCS 2019, Marburg, Germany, July 1–4, 2019, Proceedings (Lecture Notes in Computer Science #11530)
by Dominik Endres Mehwish Alam Diana ŞotropaThis book constitutes the proceedings of the 24th International Conference on Conceptual Structures, ICCS 2019, held in Marburg, Germany, in July 2019. The 14 full papers and 6 short papers presented were carefully reviewed and selected from 29 submissions. The proceedings also include one of the two invited talks. The papers focus on the representation of and reasoning with conceptual structures in a variety of contexts. ICCS 2019's theme was entitled "Graphs in Human and Machine Cognition."
Graph-Based Representation and Reasoning: 26th International Conference on Conceptual Structures, ICCS 2021, Virtual Event, September 20–22, 2021, Proceedings (Lecture Notes in Computer Science #12879)
by Nathalie Hernandez Tanya Braun Tom Hanika Marcel GehrkeThis book constitutes the proceedings of the 26th International Conference on Conceptual Structures, ICCS 2021, held virtually in September 2021.The 12 full papers and 4 short papers presented were carefully reviewed and selected from 25 submissions. The papers focus on the representation of and reasoning with conceptual structures in a variety of contexts. The papers are organized in the following topical sections: applications of conceptual structures; theory on conceptual structures, and mining conceptual structures.
Graph-Based Representations in Pattern Recognition: 14th IAPR-TC-15 International Workshop, GbRPR 2025, Caen, France, June 25–27, 2025, Proceedings (Lecture Notes in Computer Science #15727)
by Luc Brun Vincenzo Carletti Sébastien Bougleux Benoît GaüzèreThis book constitutes the refereed proceedings of the 14th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2025, held in Caen, France, in June 2025. The 25 full papers presented here were carefully reviewed and selected from 33 submissions. They are organized as per the following topical sections: Cybersecurity based on Graph models; Graph based bioinformatics; Graph similarities and graph patterns; GNN: shortcomings and solutions; Graph learning and computer vision.