Algebraic Graph Theory

Cambridge Mathematical Library

by Norman Biggs

This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. This new and enlarged edition this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.

Genres: Mathematics

214 pages, Kindle Edition

First published January 1, 1974

Reviews

[Rino Simanjuntak · Rating 3 out of 5]

I first read this book during one of my master degree classes. It was the book that introduced me to the idea behind implementing and/or applying algebraic properties, techniques, and methods to graphs. That's why it was difficult for me to understand some of the concepts and methods when reading it the first time.

I came to this book from time to time when needed, but last year I started to teach MA6281 Algebraic Graph Theory which gave me an opportunity to give a closer look. Overall, it is a good book for graduate students. It gives all the necessary backgrounds and important facts on three big ideas: linear algebra in Graph Theory, coloring problems, symmetry and regularity. It gives (mostly) sketches of proofs, which give students opportunities to think and have a deeper look into some of the theorems.

This book is a classic and so it lacks of some of the new results connected to the field. Godsil and Royle's book with the same title, for instance, gives a more cutting-edge applications.