- Table View
- List View
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 and Decomposition
by Jomon Kottarathil Sudev Naduvath Joseph Varghese KureetharaThe 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 null Lih-Hsing Hsu null 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 Jonathan L. Gross Jay Yellen Mark AndersonGraph 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 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 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 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 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 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.
Graphentheorie und Netzwerkanalyse: Eine kompakte Einführung mit Beispielen, Übungen und Lösungsvorschlägen
by Christin SchmidtDieses Lehrbuch bietet eine kompakte Einführung in die Grundlagen der Graphentheorie und die Methoden der Netzwerkanalyse. Zahlreiche praktische Beispiele und Übungsaufgaben mit Lösungsvorschlägen helfen Leser:innen dabei, die theoretischen Konzepte besser zu verstehen und anzuwenden. Dabei werden unterschiedliche Technologien und Programmiersprachen verwendet, um ein breites Spektrum an Anwendungen abzudecken. Darüber hinaus beleuchten spezielle Kapitel die Methodik mit Blick auf die Planung und Durchführung eigener Netzwerkanalyseprojekte sowie ethische und datenschutzrechtliche Aspekte. So liefert das Buch nicht nur einen theoretischen Überblick, sondern auch praktische Tipps und Anleitungen für die Untersuchung eigener netzwerkanalytischer Fragestellungen. Dieses Buch eignet sich nicht nur als Nachschlagewerk für Studierende und Dozierende vielfältiger Fachdisziplinen mit curricularem Bezug zum Thema, sondern auch als Ergänzung des Repertoires von Praktiker:innen im Bereich Data Science mit Interesse an der Untersuchung von Netzwerken. Ob als theoretischer Einstieg oder als praktischer Ratgeber - dieses Buch leistet einen Beitrag für die Untersuchung und Analyse von Netzwerken und bietet eine Grundlage für weiterführende Studien und Projekte.
Graphical Analysis of Multi-Response Data
by Kaye Enid Basford John Wilder TukeyA comprehensive summary of new and existing approaches to analyzing multiresponse data, Graphical Analysis of Multiresponse Data emphasizes graphical procedures. These procedures are then used, in various ways, to analyze, summarize, and present data from a specific, well-known plant breeding trial.These procedures result in overlap plots, their corresponding semigraphical tables, scatter plot matrices, profiles across environments and attributes for individual genotypes and groups of genotypes, and principal components.The interpretation of these displays, as an aid to understanding, is illustrated and discussed. Techniques for choosing expressions for the observed quantities are also emphasized.Graphical Analysis of Multiresponse Data is arranged into three parts:What can usefully be doneConsequences for the exampleApproaches and choices in more detailThat structure enables the reader to obtain an overview of what can be found, and to then delve into various aspects more deeply if desired. Statisticians, data analysts, biometricians, plant breeders, behavioral scientists, social scientists, and engineering scientists will find Graphical Analysis of Multiresponse Data offers invaluable assistance. Its details are also of interest to scientists in private firms, government institutions, and research organizations who are concerned with the analysis and interpretation of experimental multiresponse data.
Graphical Belief Modeling
by Russel .G AlmondThis innovative volume explores graphical models using belief functions as a representation of uncertainty, offering an alternative approach to problems where probability proves inadequate. Graphical Belief Modeling makes it easy to compare the two approaches while evaluating their relative strengths and limitations. The author examines both theory and computation, incorporating practical notes from the author's own experience with the BELIEF software package. As one of the first volumes to apply the Dempster-Shafer belief functions to a practical model, a substantial portion of the book is devoted to a single example--calculating the reliability of a complex system. This special feature enables readers to gain a thorough understanding of the application of this methodology.The first section provides a description of graphical belief models and probablistic graphical models that form an important subset: the second section discusses the algorithm used in the manipulation of graphical models: the final segment of the book offers a complete description of the risk assessment example, as well as the methodology used to describe it. Graphical Belief Modeling offers researchers and graduate students in artificial intelligence and statistics more than just a new approach to an old reliability task: it provides them with an invaluable illustration of the process of graphical belief modeling.
Graphical Data Analysis with R (Chapman & Hall/CRC The R Series #27)
by Antony UnwinSee How Graphics Reveal Information Graphical Data Analysis with R shows you what information you can gain from graphical displays. The book focuses on why you draw graphics to display data and which graphics to draw (and uses R to do so). All the datasets are available in R or one of its packages and the R code is available at rosuda.org/GDA. Graphical data analysis is useful for data cleaning, exploring data structure, detecting outliers and unusual groups, identifying trends and clusters, spotting local patterns, evaluating modelling output, and presenting results. This book guides you in choosing graphics and understanding what information you can glean from them. It can be used as a primary text in a graphical data analysis course or as a supplement in a statistics course. Colour graphics are used throughout.
Graphical Methods for Data Analysis
by J. M. ChambersThis book present graphical methods for analysing data. Some methods are new and some are old, some require a computer and others only paper and pencil; but they are all powerful data analysis tools. In many situations, a set of data � even a large set- can be adequately analysed through graphical methods alone. In most other situations, a few well-chosen graphical displays can significantly enhance numerical statistical analyses.
Graphical Models with R
by Søren Højsgaard Steffen Lauritzen David EdwardsGraphical models in their modern form have been around since the late 1970s and appear today in many areas of the sciences. Along with the ongoing developments of graphical models, a number of different graphical modeling software programs have been written over the years. In recent years many of these software developments have taken place within the R community, either in the form of new packages or by providing an R interface to existing software. This book attempts to give the reader a gentle introduction to graphical modeling using R and the main features of some of these packages. In addition, the book provides examples of how more advanced aspects of graphical modeling can be represented and handled within R. Topics covered in the seven chapters include graphical models for contingency tables, Gaussian and mixed graphical models, Bayesian networks and modeling high dimensional data.
Graphics for Statistics and Data Analysis with R (Chapman & Hall/CRC Texts in Statistical Science)
by Kevin J. Keen<i>Graphics for Statistics and Data Analysis with R, Second Edition</i>, presents the basic principles of graphical design and applies these principles to engaging examples using the graphics and lattice packages in R. It offers a wide array of modern graphical displays for data visualization and representation. Added in the second edition are coverage of the ggplot2 graphics package, material on human visualization and color rendering in R, on screen, and in print.
Graphics for Statistics and Data Analysis with R (Chapman & Hall/CRC Texts in Statistical Science)
by Kevin J. Keen<p>Graphics for Statistics and Data Analysis with R, Second Edition, presents the basic principles of graphical design and applies these principles to engaging examples using the graphics and lattice packages in R. It offers a wide array of modern graphical displays for data visualization and representation. Added in the second edition are coverage of the ggplot2 graphics package, material on human visualization and color rendering in R, on screen, and in print. It emphasizes the fundamentals of statistical graphics and best practice guidelines for producing and choosing among graphical displays in R. <p>Provides downloadable R code and data for figures at www.graphicsforstatistics.com</p>
Graphing Calculator Manual
by Kathleen Mclaughlin Dorothy Wakefield Mario F. TriolaThis manual is organized to follow the sequence of topics in the textbook, and it is an easy-to-follow, step-by-step guide on how to use the TI-83/84 Plus graphing calculator. It provides worked-out examples to help students fully understand and use the graphing calculator.
Graphs!
by David A. AdlerMath booster author David A. Adler and artist Ed Miller make pie charts easy-as-pie charts with this fun and vibrantly illustrated guide to data collection.For students, STEM topics don&’t always feel like a walk in the park. But what if they were more like a day at the fair? Follow Janet and Ben from the Ferris Wheel to the carousel as they use graphs and data collection to make decisions about their day. This is the sixteenth book in this duo&’s math picture book series. Combining elements of a graphic story with engaging and accessible nonfiction text, David A. Adler combines his well-established STEM know-how with Edward Miller&’s vibrant, high contrast art to take young readers on a wild ride through the world of bar graphs, pictographs, pie charts, and more!
Graphs, Algorithms, and Optimization (Discrete Mathematics and Its Applications)
by William Kocay Donald L. Kreher<p>Graph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NP-Completeness and polynomial reduction. A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. The book covers major areas of graph theory including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently. <p>The book also provides coverage on algorithm complexity and efficiency, NP-completeness, linear optimization, and linear programming and its relationship to graph algorithms.Written in an accessible and informal style, this work covers nearly all areas of graph theory. Graphs, Algorithms, and Optimization provides a modern discussion of graph theory applicable to mathematics, computer science, and crossover applications.</p>
Graphs, Algorithms, and Optimization (Discrete Mathematics and Its Applications)
by William Kocay Donald L. KreherThe second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs.
Graphs and Combinatorial Optimization: CTW 2023, Garmisch-Partenkirchen, Germany, June 20–22 (AIRO Springer Series #13)
by Andreas Brieden Stefan Pickl Markus SiegleThis book contains the proceedings of the 19th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, held during June 20-22, 2023, in Garmisch-Partenkirchen, Germany. This successful series of international workshops is known to attract high-quality research on the theory and application of discrete algorithms, graphs, and combinatorial optimization in a wide sense. The papers collected in this book represent cutting-edge research by leading researchers and attract a broad readership in academia worldwide. The book is addressed to researchers and advanced students, but also to professionals in industry concerned with algorithm design and optimization problems in different areas of application.
Graphs and Combinatorial Optimization: CTW2020 Proceedings (AIRO Springer Series #5)
by Claudio Gentile Giuseppe Stecca Paolo VenturaThis book highlights new and original contributions on Graph Theory and Combinatorial Optimization both from the theoretical point of view and from applications in all fields. The book chapters describe models and methods based on graphs, structural properties, discrete optimization, network optimization, mixed-integer programming, heuristics, meta-heuristics, math-heuristics, and exact methods as well as applications. The book collects selected contributions from the CTW2020 international conference (18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization), held online on September 14-16, 2020. The conference was organized by IASI-CNR with the contribution of University of Roma Tre, University Roma Tor Vergata, and CNRS-LIX and with the support of AIRO. It is addressed to researchers, PhD students, and practitioners in the fields of Graph Theory, Discrete Mathematics, Combinatorial Optimization, and Operations Research.
Graphs and Matrices
by Ravindra B. BapatThis 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 reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.