Introduction to Graph Theory by Douglas B. West: A Comprehensive Textbook for Students and Researchers
Graph theory is a branch of mathematics that studies the properties and applications of graphs, which are abstract structures that consist of vertices (or nodes) and edges (or links) connecting them. Graphs can model many phenomena in science, engineering, social sciences, and computer science, such as networks, algorithms, optimization, coloring, games, cryptography, and more.
introduction to graph theory douglas west pdf
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One of the most popular and widely used 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 the basic concepts and techniques of graph theory, as well as some advanced topics 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:
Fundamental Concepts
Trees and Distance
Matchings and Factors
Connectivity and Paths
Eulerian and Hamiltonian Graphs
Planar Graphs
Coloring of Graphs
Digraphs
Additional Topics
The book also contains an appendix with some mathematical background, a glossary of terms, a list of symbols, a bibliography, an index, and a list of 1296 exercises with varying levels of difficulty. The book also has 447 figures to illustrate the concepts and examples.
The book is praised for its clarity, rigor, breadth, depth, and pedagogy. It provides a comprehensive introduction to graph theory that balances theory and practice. It also exposes the reader to some current research topics and open problems in graph theory. The book is suitable for self-study or as a textbook for a course on graph theory.
The book is available in hardcover or paperback format from various online retailers or libraries. It can also be downloaded as a PDF file from some websites[^2^] [^1^], but this may violate the author's or publisher's rights. The official website of the book[^3^] provides some additional resources, such as errata, solutions to selected exercises, lecture notes, slides, software, and links to other graph theory websites.
Some of the topics that the book covers in more detail are:
The structure and properties of trees, spanning trees, minimum spanning trees, and shortest paths.
The existence and algorithms for finding matchings, perfect matchings, maximum matchings, and factors in graphs.
The notions and criteria of connectivity, edge-connectivity, vertex-connectivity, blocks, cut-vertices, bridges, Menger's theorem, network flows, and augmenting paths.
The characterization and enumeration of Eulerian and Hamiltonian graphs, the Chinese postman problem, the traveling salesman problem, and Dirac's theorem.
The definition and classification of planar graphs, Euler's formula, Kuratowski's theorem, dual graphs, embeddings, faces, and the four-color theorem.
The concepts and methods of graph coloring, such as chromatic number, chromatic polynomial, Brooks' theorem, Vizing's theorem, list coloring, interval graphs, perfect graphs, and Ramsey theory.
The generalization of graphs to digraphs (directed graphs), such as tournaments, acyclic digraphs, reachability, topological sorting, strongly connected components, and digraph coloring.
Some additional topics that are not covered in depth in the book but are briefly introduced or mentioned, such as matroids, extremal graph theory, random graphs, algebraic graph theory, spectral graph theory, graph minors, graph drawing, and computational complexity.
The book assumes that the reader has some familiarity with basic mathematical concepts and techniques, such as sets, functions, relations, induction, proof methods, logic, combinatorics, matrices, and algorithms. The book also uses some notation and terminology from abstract algebra and linear algebra. However, the book provides some review and explanation of these topics in the appendix and throughout the text. The book also provides many examples and exercises to help the reader understand and apply the concepts and techniques of graph theory.
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