Graph theory continues to be one of the fastest growing areas of modern mathematics because of its wide applicability in such diverse disciplines as computer science, engineering, chemistry, management science, social science, and resource planning. Graphs arise as mathematical models in these fields, and the theory of graphs provides a spectrum of methods of proof. This concisely written textbook is intended for an introductory course in graph theory for undergraduate mathematics majors or advanced undergraduate and graduate students from the many fields that benefit from graph-theoretic applications.

This second edition includes new chapters on labeling and communications networks and small-worlds, as well as expanded beginner's material in the early chapters, including more examples, exercises, hints and solutions to key problems. Many additional changes, improvements, and corrections resulting from classroom use and feedback have been added throughout. With a distinctly applied flavor, this gentle introduction to graph theory consists of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little mathematical maturity are the only prerequisites.

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

Autorentext

W. D. Wallis served as a Professor of Mathematics at Southern Illinois University, Carbondale, for 24 years up until his retirement in 2009. Before that he taught for 15 years at the University of Newcastle, Australia, and for 4 years at La Trobe University, Australia. His main areas of research have been in Combinatorial Mathematics and Graph Theory. He has also published some work in Computer Science and in Algebra. He has authored or co-authored fourteen books on Mathematics, together with some second editions, and edited nine books. He has published 268 research articles and book chapters.

Inhalt
Graphs.- Walks, Paths and Cycles.- Connectivity.- Trees.- Linear Spaces Associated with Graphs.- Factorizations.- Graph Colorings.- Planarity.- Labeling.- Ramsey Theory.- Digraphs.- Critical Paths.- Flows in Networks.- Computational Considerations.- Communications Networks and Small-Worlds.