Algebraic graph theory
 Author/Creator
 Biggs, Norman.
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Cambridge : Cambridge University Press 1993.
 Physical description
 vi, 205 p. ; 23 cm.
 Series
 Cambridge mathematical library
Access
Available online

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QA166 .B53 1993

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QA166 .B53 1993

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QA166 .B53 1993
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. [191]201) and index.
 Contents

 1. 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 treenumber 7. Determinant expansions 8. Vertexpartitions 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. Vertextransitive graphs 17. Symmetric graphs 18. Symmetric graphs of degree three 19. The covering graph construction 20. Distancetransitive graphs 21. Feasibility of intersection arrays 22. Imprimitivity 23. Minimal regular graphs with given girth References Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This is a substantial revision of a muchquoted 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Graph theory.
Bibliographic information
 Publication date
 1993
 Responsibility
 Norman Biggs.
 ISBN
 0521458978
 9780521458979