Applied Graph Theory An Introduction With Graph Optimization And Algebraic Graph Theory

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Applied Graph Theory: An Introduction With Graph Optimization And Algebraic Graph Theory

Christopher H Griffin
Applied Graph Theory An Introduction With Graph Optimization And Algebraic Graph Theory Book PDF

Author : Christopher H Griffin
Publisher : World Scientific
Page : 305 pages
File Size : 54,8 Mb
Release : 2023-08-08
Category : Mathematics
ISBN : 9789811273124

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Applied Graph Theory: An Introduction With Graph Optimization And Algebraic Graph Theory by Christopher H Griffin Pdf

This book serves as an introduction to graph theory and its applications. It is intended for a senior undergraduate course in graph theory but is also appropriate for beginning graduate students in science or engineering. The book presents a rigorous (proof-based) introduction to graph theory while also discussing applications of the results for solving real-world problems of interest. The book is divided into four parts. Part 1 covers the combinatorial aspects of graph theory including a discussion of common vocabulary, a discussion of vertex and edge cuts, Eulerian tours, Hamiltonian paths and a characterization of trees. This leads to Part 2, which discusses common combinatorial optimization problems. Spanning trees, shortest path problems and matroids are all discussed, as are maximum flow problems. Part 2 ends with a discussion of graph coloring and a proof of the NP-completeness of the coloring problem. Part 3 introduces the reader to algebraic graph theory, and focuses on Markov chains, centrality computation (e.g., eigenvector centrality and page rank), as well as spectral graph clustering and the graph Laplacian. Part 4 contains additional material on linear programming, which is used to provide an alternative analysis of the maximum flow problem. Two appendices containing prerequisite material on linear algebra and probability theory are also provided.

Applied Graph Theory

Christopher Griffin
Applied Graph Theory Book PDF

Author : Christopher Griffin
Publisher : World Scientific Publishing Company
Page : 0 pages
File Size : 48,6 Mb
Release : 2023-08
Category : Graph theory
ISBN : 9811273103

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Applied Graph Theory by Christopher Griffin Pdf

This book serves as an introduction to graph theory and its applications. It is intended for a senior undergraduate course in graph theory but is also appropriate for beginning graduate students in science or engineering. The book presents a rigorous (proof-based) introduction to graph theory while also discussing applications of the results for solving real-world problems of interest. The book is divided into four parts. Part 1 covers the combinatorial aspects of graph theory including a discussion of common vocabulary, a discussion of vertex and edge cuts, Eulerian tours, Hamiltonian paths and a characterization of trees. This leads to Part 2, which discusses common combinatorial optimization problems. Spanning trees, shortest path problems and matroids are all discussed, as are maximum flow problems. Part 2 ends with a discussion of graph coloring and a proof of the NP-completeness of the coloring problem. Part 3 introduces the reader to algebraic graph theory, and focuses on Markov chains, centrality computation (e.g., eigenvector centrality and page rank), as well as spectral graph clustering and the graph Laplacian. Part 4 contains additional material on linear programming, which is used to provide an alternative analysis of the maximum flow problem. Two appendices containing prerequisite material on linear algebra and probability theory are also provided.

Topics in Algebraic Graph Theory

Lowell W. Beineke,Robin J. Wilson
Topics in Algebraic Graph Theory Book PDF

Author : Lowell W. Beineke,Robin J. Wilson
Publisher : Cambridge University Press
Page : 302 pages
File Size : 45,9 Mb
Release : 2004-10-04
Category : Mathematics
ISBN : 0521801974

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Topics in Algebraic Graph Theory by Lowell W. Beineke,Robin J. Wilson Pdf

There is no other book with such a wide scope of both areas of algebraic graph theory.

Algebraic Graph Theory

Chris Godsil,Gordon F. Royle
Algebraic Graph Theory Book PDF

Author : Chris Godsil,Gordon F. Royle
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 51,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461301639

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Algebraic Graph Theory by Chris Godsil,Gordon F. Royle Pdf

This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.

Graph Theory

Karin R Saoub
Graph Theory Book PDF

Author : Karin R Saoub
Publisher : CRC Press
Page : 421 pages
File Size : 40,5 Mb
Release : 2021-03-17
Category : Mathematics
ISBN : 9780429779886

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Graph Theory by Karin R Saoub Pdf

Graph 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.

Graphs, Algorithms, and Optimization

William Kocay,Donald L. Kreher
Graphs Algorithms and Optimization Book PDF

Author : William Kocay,Donald L. Kreher
Publisher : CRC Press
Page : 504 pages
File Size : 47,8 Mb
Release : 2017-09-20
Category : Mathematics
ISBN : 9781351989121

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Graphs, Algorithms, and Optimization by William Kocay,Donald L. Kreher Pdf

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. 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.

Topics in Graph Theory

Jonathan L Gross,Jay Yellen,Mark Anderson
Topics in Graph Theory Book PDF

Author : Jonathan L Gross,Jay Yellen,Mark Anderson
Publisher : CRC Press
Page : 904 pages
File Size : 46,7 Mb
Release : 2023-05-24
Category : Mathematics
ISBN : 9781000884081

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Topics in Graph Theory by Jonathan L Gross,Jay Yellen,Mark Anderson Pdf

The interplay continues to grow between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences. Topics in Graph Theory is geared toward the more mathematically mature student. The first three chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level. The authors build upon material previously published in Graph Theory and Its Applications, Third Edition, by the same authors. That text covers material for both an undergraduate and graduate course, while this book builds on and expands the graduate-level material. Features Extensive exercises and applications. Flexibility: appropriate for either a first course at the graduate level or an advanced course at the undergraduate level. Opens avenues to a variety of research areas in graph theory. Emphasis on topological and algebraic graph theory.

Introductory Graph Theory

Gary Chartrand
Introductory Graph Theory Book PDF

Author : Gary Chartrand
Publisher : Courier Corporation
Page : 320 pages
File Size : 48,9 Mb
Release : 2012-04-30
Category : Science
ISBN : 9780486134949

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Introductory Graph Theory by Gary Chartrand Pdf

Clear, lively style covers all basics of theory and application, including mathematical models, elementary graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, more.

A Beginner's Guide to Graph Theory

W.D. Wallis
A Beginner s Guide to Graph Theory Book PDF

Author : W.D. Wallis
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 44,7 Mb
Release : 2010-05-05
Category : Mathematics
ISBN : 9780817645809

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A Beginner's Guide to Graph Theory by W.D. Wallis Pdf

Concisely written, gentle introduction to graph theory suitable as a textbook or for self-study Graph-theoretic applications from diverse fields (computer science, engineering, chemistry, management science) 2nd ed. includes new chapters on labeling and communications networks and small worlds, as well as expanded beginner's material Many additional changes, improvements, and corrections resulting from classroom use

Handbook of Graph Theory, Combinatorial Optimization, and Algorithms

Krishnaiyan "KT" Thulasiraman,Subramanian Arumugam,Andreas Brandstädt,Takao Nishizeki
Handbook of Graph Theory Combinatorial Optimization and Algorithms Book PDF

Author : Krishnaiyan "KT" Thulasiraman,Subramanian Arumugam,Andreas Brandstädt,Takao Nishizeki
Publisher : CRC Press
Page : 1217 pages
File Size : 40,5 Mb
Release : 2016-01-05
Category : Computers
ISBN : 9781420011074

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Handbook of Graph Theory, Combinatorial Optimization, and Algorithms by Krishnaiyan "KT" Thulasiraman,Subramanian Arumugam,Andreas Brandstädt,Takao Nishizeki Pdf

The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c

Handbook of Graph Theory, Second Edition

Jonathan L. Gross,Jay Yellen,Ping Zhang
Handbook of Graph Theory Second Edition Book PDF

Author : Jonathan L. Gross,Jay Yellen,Ping Zhang
Publisher : CRC Press
Page : 1634 pages
File Size : 54,6 Mb
Release : 2013-12-17
Category : Mathematics
ISBN : 9781439880180

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Handbook of Graph Theory, Second Edition by Jonathan L. Gross,Jay Yellen,Ping Zhang Pdf

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 extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

Graph Theory

Adrian Bondy,U.S.R. Murty
Graph Theory Book PDF

Author : Adrian Bondy,U.S.R. Murty
Publisher : Springer
Page : 0 pages
File Size : 43,9 Mb
Release : 2010-10-19
Category : Mathematics
ISBN : 1849966907

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Graph Theory by Adrian Bondy,U.S.R. Murty Pdf

The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory.

Graph Theory

Beril Sirmacek
Graph Theory Book PDF

Author : Beril Sirmacek
Publisher : BoD – Books on Demand
Page : 196 pages
File Size : 48,9 Mb
Release : 2018-01-31
Category : Mathematics
ISBN : 9789535137726

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Graph Theory by Beril Sirmacek Pdf

This book is prepared as a combination of the manuscripts submitted by respected mathematicians and scientists around the world. As an editor, I truly enjoyed reading each manuscript. Not only will the methods and explanations help you to understand more about graph theory, but I also hope you will find it joyful to discover ways that you can apply graph theory in your scientific field. I believe the book can be read from the beginning to the end at once. However, the book can also be used as a reference guide in order to turn back to it when it is needed. I have to mention that this book assumes the reader to have a basic knowledge about graph theory. The very basics of the theory and terms are not explained at the beginner level. I hope this book will support many applied and research scientists from different scientific fields.

Graph Theory

B Andrasfai
Graph Theory Book PDF

Author : B Andrasfai
Publisher : CRC Press
Page : 298 pages
File Size : 45,8 Mb
Release : 1991-01-01
Category : Mathematics
ISBN : 0852742223

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Graph Theory by B Andrasfai Pdf

Graph Theory: Flows, Matrices covers a number of topics in graph theory that are important in the major areas of application. It provides graph theoretic tools that can be readily and efficiently applied to problems in operational research, computer science, electrical engineering, and economics. Emphasizing didactic principles, the book derives theorems and proofs from a detailed analysis of the structure of graphs. The easy-to-follow algorithms can be readily converted to computer codes in high-level programming languages. Requiring knowledge of the basic concepts of graph theory and a familiarity with some simple results, the book also includes 100 exercises with solutions to help readers gain experience and 131 diagrams to aid in the understanding of concepts and proofs.

Graphs, Networks and Algorithms

Dieter Jungnickel
Graphs Networks and Algorithms Book PDF

Author : Dieter Jungnickel
Publisher : Springer Science & Business Media
Page : 677 pages
File Size : 46,6 Mb
Release : 2012-11-08
Category : Mathematics
ISBN : 9783642322785

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Graphs, Networks and Algorithms by Dieter Jungnickel Pdf

From the reviews of the previous editions ".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..." K.Engel, Mathematical Reviews 2002 The substantial development effort of this text, involving multiple editions and trailing in the context of various workshops, university courses and seminar series, clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended. P .B. Gibbons, Zentralblatt für Mathematik 2005 Once again, the new edition has been thoroughly revised. In particular, some further material has been added: more on NP-completeness (especially on dominating sets), a section on the Gallai-Edmonds structure theory for matchings, and about a dozen additional exercises – as always, with solutions. Moreover, the section on the 1-factor theorem has been completely rewritten: it now presents a short direct proof for the more general Berge-Tutte formula. Several recent research developments are discussed and quite a few references have been added.