代数图论 Algebraic Graph Theory 英文原版 Norman Biggs 代数 数论与组合理论

基本信息

Format:Paperback / softback 216 pages, 18 Line drawings, unspecified

Publisher:Cambridge University Press

Imprint:Cambridge University Press

Edition:2 Revised edition

ISBN:9780521458979

Published:3 Feb 1994

Classifications:Algebra, Combinatorics & graph theory

Readership:Professional & Vocational

Weight:326g

Dimensions:226 x 150 x 13 (mm)

书籍信息仅供参考，具体以实物为准

书籍简介

这是对1974年出版的一本被广泛引用的专著的实质性修订。结构未变，但文本已被澄清，符号也与当前的实践相一致。在每一章的末尾都有大量的 "附加结果"，从而涵盖了过去20年的大部分主要进展。

比格斯教授的基本目标仍然是用代数术语表达图形的属性，然后推导出关于它们的定理。在开头部分，他讨论了线性代数和矩阵理论在图形研究中的应用；深入讨论了邻接矩阵和入射矩阵等代数结构及其应用。接下来是对色度多项式理论的广泛阐述，这一主题与理论物理学中研究的 "交互模型 "和结的理论有着密切的联系。

结尾一部分是关于对称性和规律性属性。这里与代数组合学和群论的其他分支有重要联系。这个新的和扩大的版本将是广大数学家、计算机科学家和理论物理学家的基本读物。

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.

作者简介

诺曼-林斯特德-比格斯（生于1941年1月2日）是英国知名数学家，专注于离散数学，特别是代数组合学。

Norman Linstead Biggs (born 2 January 1941) is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics