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  3. Algebraic Graph Theory
  • Cited by 619
  • 2nd edition
  • Norman Biggs, London School of Economics and Political Science
Publisher:
Cambridge University Press
Online publication date:
August 2012
Print publication year:
1974
Online ISBN:
9780511608704
DOI:
https://doi.org/10.1017/CBO9780511608704
Subjects:
Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding
Series:
Cambridge Mathematical Library (67)
Information

Book description

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.

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