Introduction To Graph Theory Douglas West Pdf
Introduction to Graph Theory by Douglas B. West
Graph theory is a branch of mathematics that studies the properties and applications of graphs, which are abstract structures that consist of vertices and edges connecting them. Graphs can be used to model many phenomena in science, engineering, social sciences, and computer science, such as networks, algorithms, cryptography, games, coloring, and optimization.
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One of the most popular and comprehensive textbooks on graph theory is Introduction to Graph Theory by Douglas B. West, a professor of mathematics at the University of Illinois at Urbana-Champaign. The book was first published in 1996 by Prentice Hall and has since been revised and updated in a second edition in 2001. The book covers a wide range of topics in graph theory, from basic concepts and definitions to advanced results and applications. The book is suitable for undergraduate and graduate students, as well as researchers and practitioners who want to learn more about graph theory.
The book is divided into nine chapters, each with several sections and subsections. The chapters are as follows:
Chapter 1: Fundamental Concepts. This chapter introduces the basic notions and terminology of graph theory, such as adjacency, degree, isomorphism, subgraphs, paths, cycles, trees, connectivity, Eulerian and Hamiltonian graphs, planarity, and colorability.
Chapter 2: Trees and Distance. This chapter focuses on the properties and applications of trees, which are graphs without cycles. The chapter covers topics such as spanning trees, minimum spanning trees, distance functions, centers and medians, eccentricity sequences, Wiener index, Cayley's formula, Prufer codes, and tree-decompositions.
Chapter 3: Matchings and Factors. This chapter studies the problem of finding subsets of edges that cover vertices in a graph. The chapter covers topics such as matchings, Hall's theorem, Tutte's theorem, König's theorem, factors, factor-critical graphs, perfect matchings, Petersen's theorem, Edmonds' algorithm, and Tutte-Berge formula.
Chapter 4: Connectivity and Paths. This chapter investigates the notion of connectivity in graphs, which measures how strongly the vertices are linked by paths. The chapter covers topics such as cut-vertices and blocks, Menger's theorem, edge-connectivity and line graphs, k-connected graphs and Whitney's theorem, network flows and Ford-Fulkerson algorithm, max-flow min-cut theorem, integral flows and flows with gains.
Chapter 5: Coloring of Graphs. This chapter explores the problem of coloring the vertices or edges of a graph with a minimum number of colors such that no two adjacent elements have the same color. The chapter covers topics such as chromatic number and chromatic polynomial, Brooks' theorem and Vizing's theorem, independent sets and cliques, perfect graphs and strong perfect graph theorem, interval graphs and chordal graphs, list coloring and choosability, edge-coloring and total-coloring.
Chapter 6: Planar Graphs. This chapter examines the special class of graphs that can be drawn on a plane without crossing edges. The chapter covers topics such as Euler's formula and Platonic solids, Kuratowski's theorem and Wagner's theorem, dual graphs and duality, faces and facial walks, embeddings and rotations, crossing number and thickness, geometric graphs and Delaunay triangulations.
Chapter 7: Edges and Cycles. This chapter deals with the properties and applications of edges and cycles in graphs. The chapter covers topics such as edge-disjoint cycles and ear decompositions, Hamiltonian cycles and Dirac's theorem, Ore's theorem and Bondy-Chvátal theorem, Hamiltonian paths and closure, cycle space and cycle basis, girth and circumference, toughness and Chvátal-Erdős condition.
Chapter 8: Additional Topics. This chapter presents some additional topics in graph theory that are not covered in the previous chapters. The chapter covers topics such as Ramsey theory and Ramsey numbers, Turán's theorem and extremal graph theory, random graphs and Erdős-Rényi model, probabilistic methods and Lovász local lemma, algebraic methods and eigenvalues, spectral graph theory and expander graphs, graph minors and Robertson-Seymour theorem.
Chapter 9: Digraphs and Hypergraphs. This chapter introduces two generalizations of graphs, namely digraphs and hypergraphs. Digraphs are graphs with directed edges, and hypergraphs are graphs with edges that can connect more than two vertices. The chapter covers topics such as directed paths and cycles, tournaments and transitive closure, acyclic digraphs and topological sorting, strongly connected components and condensation, reachability and connectivity, hypergraphs and incidence matrices, matchings and transversals in hypergraphs.
The book also contains an appendix with a summary of notation, a glossary of terms, a list of symbols, and a table of NP-completeness results. The book has 1296 exercises, 447 figures, and 28 tables. The book also provides references to the literature and historical notes on the development of graph theory.
The book is available in both hardcover and paperback editions. The book can also be accessed online in PDF format from various sources . However, the author and publisher do not endorse or authorize the distribution of the PDF files, and they may contain errors or omissions. The author and publisher recommend purchasing the official printed version of the book for the best quality and accuracy.
Introduction to Graph Theory by Douglas B. West is a comprehensive and authoritative textbook on graph theory that covers both classical and modern topics. The book is suitable for anyone who wants to learn more about graph theory, from students to researchers to practitioners. The book is well-written, well-organized, well-illustrated, and well-exercised. The book is a valuable resource for anyone interested in graph theory.