Graphs & Digraphs, Seventh Edition masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. This classic text, widely popular among students and instructors alike for decades, is thoroughly streamlined in this new, seventh edition, to present a text consistent with contemporary expectations.Changes and updates to this edition include:A rewrite of four chapters from the ground upStreamlining by over a third for efficient, comprehensive coverage of graph theoryFlexible structure with foundational Chapters 1–6 and customizable topics in Chapters 7–11Incorporation of the latest developments in fundamental graph theoryStatements of recent groundbreaking discoveries, even if proofs are beyond scopeCompletely reorganized chapters on traversability, connectivity, coloring, and extremal graph theory to reflect recent developmentsThe text remains the consummate choice for an advanced undergraduate level or introductory graduate-level course exploring the subject’s fascinating history, while covering a host of interesting problems and diverse applications. Our major objective is to introduce and treat graph theory as the beautiful area of mathematics we have always found it to be. We have striven to produce a reader-friendly, carefully written book that emphasizes the mathematical theory of graphs, in all their forms. While a certain amount of mathematical maturity, including a solid understanding of proof, is required to appreciate the material, with a small number of exceptions this is the only pre-requisite.In addition, owing to the exhilarating pace of progress in the field, there have been countless developments in fundamental graph theory ever since the previous edition, and many of these discoveries have been incorporated into the book. Of course, some of the proofs of these results are beyond the scope of the book, in which cases we have only included their statements. In other cases, however, these new results have led us to completely reorganize our presentation. Two examples are the chapters on coloring and extremal graph theory.
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Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory.
Les mer
1 Graphs1.1 Fundamentals1.2 Isomorphism1.3 Families of graphs1.4 Operations on graphs1.5 Degree sequences1.6 Path and cycles1.7 Connected graphs and distance1.8 Trees and forests1.9 Multigraphs and pseudographs2 Digraphs2.1 Fundamentals2.2 Strongly connected digraphs2.3 Tournaments2.4 Score sequences3 Traversability3.1 Eulerian graphs and digraphs3.2 Hamiltonian graphs3.3 Hamiltonian digraphs3.4 Highly hamiltonian graphs3.5 Graph powers4 Connectivity4.1 Cut-vertices, bridges, and blocks4.2 Vertex connectivity4.3 Edge-connectivity4.4 Menger's theorem5 Planarity5.1 Euler's formula5.2 Characterizations of planarity5.3 Hamiltonian planar graphs5.4 The crossing number of a graph6 Coloring6.1 Vertex coloring6.2 Edge coloring6.3 Critical and perfect graphs6.4 Maps and planar graphs7 Flows7.1 Networks7.2 Max-flow min-cut theorem7.3 Menger's theorems for digraphs7.4 A connection to coloring8 Factors and covers8.1 Matchings and 1-factors8.2 Independence and covers8.3 Domination8.4 Factorizations and decompositions8.5 Labelings of graphs9 Extremal graph theory9.1 Avoiding a complete graph9.2 Containing cycles and trees9.3 Ramsey theory9.4 Cages and Moore graphs10 Embeddings10.1 The genus of a graph10.2 2-Cell embeddings of graphs10.3 The maximum genus of a graph10.4 The graph minor theorem11 Graphs and algebra11.1 Graphs and matrices11.2 The automorphism group11.3 Cayley color graphs11.4 The reconstruction problem
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Produktdetaljer

ISBN
9781032133409
Publisert
2024-01-23
Utgave
7. utgave
Utgiver
Vendor
Chapman & Hall/CRC
Vekt
453 gr
Høyde
234 mm
Bredde
156 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
354

Om bidragsyterne

Gary Chartrand is professor emeritus at Western Michigan University. He was awarded all three of his university degrees in mathematics from Michigan State University. His main interest in mathematics has always been graph theory.

He has authored or co-authored over 300 research articles in graph theory. He served as the first managing editor of the Journal of Graph Theory (for seven years) and was a member of the editorial boards of the Journal of Graph Theory and Discrete Mathematics. He served as a vice president of the Institute of Combinatorics and Its Applications. He directed the dissertations of 22 doctoral students at Western Michigan University.

He is the recipient of the University Distinguished Faculty Scholar Award and the Alumni Association Teaching Award from Western Michigan University and the Distinguished Faculty Award from the State of Michigan. He also received an award as managing editor of the best new journal (Journal of Graph Theory) by the Association of American Publishers in the scientific, medical, and technical category.

Heather Jordon earned her PhD in mathematics from Western Michigan University in 1996 under the direction of Gary Chartrand. She is currently an Associate Editor for Mathematical Reviews, produced by the American Mathematical Society.

Vincent Vatter earned his PhD in mathematics from Rutgers University in 2006, studying under Doron Zeilberger. Prior to that, he received his bachelor's degree in mathematics from Michigan State University in 2001. Currently, he is a professor of mathematics at the University of Florida, where he resides with his two daughters, Madison and Vienna. He has authored or co-authored over 60 research articles in enumerative combinatorics, graph theory, order theory, and theoretical computer science, and has directed the dissertations of five doctoral students.

Ping Zhang earned her PhD in mathematics from Michigan State University. After spending a year at the University of Texas at El Paso, she joined Western Michigan University, where she currently serves as a professor. In 2017, she was named a Distinguished University Faculty Scholar. Her primary research interests are in algebraic combinatorics and graph theory.

Dr. Zhang has co-authored six textbooks, notably Graphs & Digraphs and Chromatic Graph Theory, and is a co-editor of The Handbook of Graph Theory, Second Edition, all published by CRC Press. She has also authored or co-authored over 340 research articles and given more than 80 talks at various universities and conferences. At Western Michigan University, she has directed the dissertations of 26 doctoral students.