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Original Essays | May 1, 2013
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Other titles in the Cambridge Mathematical Library series:
Algebraic Graph Theory (Cambridge Mathematical Library)by Norman L. Biggs
Synopses & ReviewsPublisher Comments: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.
Synopsis:A revision of an important textbook: essential reading for all combinatorialists.
Synopsis:A revision of an important textbook: essential reading for all combinatorialists.
Synopsis:In this substantial revision of his excellent book, Professor Biggs has taken the opportunity to clarify and update the text, whilst leaving the structure unchanged. Like the first edition, this will be essential reading for all combinatorialists.
Synopsis:This substantial revision of a much-quoted monograph--originally published in 1974--aims to express properties of graphs in algebraic terms, then to deduce theorems about them. Although the structure of the volume is unchanged, the text has been clarified and the notation brought into line with current practice.
Table of Contents1. Introduction to algebraic graph theory; Part I. Linear Algebra in Graphic Thoery: 2. The spectrum of a graph; 3. Regular graphs and line graphs; 4. Cycles and cuts; 5. Spanning trees and associated structures; 6. The tree-number; 7. Determinant expansions; 8. Vertex-partitions and the spectrum; Part II. Colouring Problems: 9. The chromatic polynomial; 10. Subgraph expansions; 11. The multiplicative expansion; 12. The induced subgraph expansion; 13. The Tutte polynomial; 14. Chromatic polynomials and spanning trees; Part III. Symmetry and Regularity: 15. Automorphisms of graphs; 16. Vertex-transitive graphs; 17. Symmetric graphs; 18. Symmetric graphs of degree three; 19. The covering graph construction; 20. Distance-transitive graphs; 21. Feasibility of intersection arrays; 22. Imprimitivity; 23. Minimal regular graphs with given girth; References; Index.
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