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Algebraic Graph Theory (Cambridge Mathematical Library)

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Algebraic Graph Theory (Cambridge Mathematical Library) Cover

ISBN13: 9780521458979
ISBN10: 0521458978
Condition:
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Synopses & Reviews

Publisher 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 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 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.

What Our Readers Are Saying

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Average customer rating based on 2 comments:

teja, May 14, 2008 (view all comments by teja)
simple, densed & interesting
Was this comment helpful? | Yes | No
(1 of 1 readers found this comment helpful)
saptakrish, June 26, 2007 (view all comments by saptakrish)
This book is very much math oriented and the graph theory is nothing but the picture of mathematics. I like it very much. This book is excellent. We are working on this field. This will help us a lot.
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Product Details

ISBN:
9780521458979
Author:
Biggs, Norman
Author:
Biggs
Author:
Norman, Biggs
Author:
Biggs, Norman
Publisher:
Cambridge University Press
Location:
Cambridge :
Subject:
Graphic Methods
Subject:
Probability
Subject:
Graph theory
Subject:
General Mathematics
Subject:
Mathematics - General
Subject:
Discrete Mathematics
Edition Number:
2
Edition Description:
Trade paper
Series:
Cambridge mathematical library
Series Volume:
v. 4-5
Publication Date:
19940231
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
18 b/w illus.
Pages:
216
Dimensions:
8.84x6.22x.56 in. .81 lbs.

Related Subjects

History and Social Science » World History » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Combinatorics
Science and Mathematics » Mathematics » General

Algebraic Graph Theory (Cambridge Mathematical Library) New Trade Paper
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$72.50 In Stock
Product details 216 pages Cambridge University Press - English 9780521458979 Reviews:
"Synopsis" by , A revision of an important textbook: essential reading for all combinatorialists.
"Synopsis" by , A revision of an important textbook: essential reading for all combinatorialists.
"Synopsis" by , 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" by , 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.
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