Chartrand G. Graphs and Digraphs 7ed 2024

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Chartrand G. Graphs and Digraphs 7ed 2024

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Textbook in PDF format 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 developments The 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. Preface to the seventh edition About the authors Graphs Fundamentals Isomorphism Families of graphs Operations on graphs Degree sequences Path and cycles Connected graphs and distance Trees and forests Multigraphs and pseudographs Exercises Digraphs Fundamentals Strongly connected digraphs Tournaments Score sequences Exercises Traversability Eulerian graphs and digraphs Hamiltonian graphs Hamiltonian digraphs Highly hamiltonian graphs Graph powers Exercises Connectivity Cut-vertices, bridges, and blocks Vertex connectivity Edge-connectivity Menger's theorem Exercises Planarity Euler's formula Characterizations of planarity Hamiltonian planar graphs The crossing number of a graph Exercises Coloring Vertex coloring Edge coloring Critical and perfect graphs Maps and planar graphs Exercises Flows Networks Max-flow min-cut theorem Menger's theorems for digraphs A connection to coloring Exercises Factors and covers Matchings and 1-factors Independence and covers Domination Factorizations and decompositions Labelings of graphs Exercises Extremal graph theory Avoiding a complete graph Containing cycles and trees Ramsey theory Cages and Moore graphs Exercises Embeddings The genus of a graph 2-Cell embeddings of graphs The maximum genus of a graph The graph minor theorem Exercises Graphs and algebra Graphs and matrices The automorphism group Cayley color graphs The reconstruction problem Exercises Hints to selected exercises Bibliography Index