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Algebraic Graph Theory : Cambridge Mathematical Library - Norman Biggs

Algebraic Graph Theory

Cambridge Mathematical Library

Paperback

Published: 4th April 1994
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In this substantial revision of a much-quoted monograph first published in 1974, Dr. Biggs aims to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first section, 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 that 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. The structure of the volume 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 past twenty years. This new and enlarged edition will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.

Introduction to algebraic graph theory
Linear Algebra in Graphic Thoery
The spectrum of a graph
Regular graphs and line graphs
Cycles and cuts
Spanning trees and associated structures
The tree-number
Determinant expansions
Vertex-partitions and the spectrum
Colouring Problems
The chromatic polynomial
Subgraph expansions
The multiplicative expansion
The induced subgraph expansion
The Tutte polynomial
Chromatic polynomials and spanning trees
Symmetry and Regularity
Automorphisms of graphs
Vertex-transitive graphs
Symmetric graphs
Symmetric graphs of degree three
The covering graph construction
Distance-transitive graphs
Feasibility of intersection arrays
Imprimitivity
Minimal regular graphs with given girth
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521458979
ISBN-10: 0521458978
Series: Cambridge Mathematical Library
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 216
Published: 4th April 1994
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.6 x 15.2  x 1.4
Weight (kg): 0.34
Edition Number: 2
Edition Type: Revised