Algebraic Graph Theory (Cambridge Mathematical Library) [Paperback]

Norman Biggs (Author)

Book Description

ISBN-10: 0521458978 | ISBN-13: 978-0521458979 | Publication Date: February 25, 1994 | Edition: 2

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.

Editorial Reviews

Book Description

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.

Product Details

• Paperback: 216 pages
• Publisher: Cambridge University Press; 2 edition (February 25, 1994)
• Language: English
• ISBN-10: 0521458978
• ISBN-13: 978-0521458979
• Product Dimensions: 8.9 x 6 x 0.6 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #633,046 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

24 of 24 people found the following review helpful:

4.0 out of 5 stars Well written, intriguing, but somewhat dated, October 18, 2002

By 

Todd Ebert (Long Beach California) - See all my reviews

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This review is from: Algebraic Graph Theory (Cambridge Mathematical Library) (Paperback)

I found this book very clear, concise, and well written. Most proofs seemed effortless on both the author's and reader's part. Moreover, I found the content very interesting, especially the results on the spectrum of a graph, which simply represents the eigenvalues (and their multiplicities) of the adjacency matrix (although recently it has been defined in terms of the normalized incidence matrix). It amazed me just how much mathematics can be put to bear on such a simple notion of vertices and connections between them. The only downside to this book is that algebraic graph theory has moved in many new directions since the first edition (the second edition mostly states some recent results at the end of each chapter), and the interested reader may want to supplement this book or follow up this book with the following: "Spectral Graph Theory", by Fan Chung, "Algebraic Graph Theory", by Godsil et al., and "Modern Graph Theory", by Bollobas, all of which make for graduate-level reading. And to think that some mathematics departments still show little if any desire to support fellow mathematicians who study graph theory! Reading any of these books hopefully might alter some of those entrenched attitudes.

1 of 1 people found the following review helpful:

4.0 out of 5 stars Clear and (mostly) to the point, February 22, 2010

By 

Narada "the wondering jew" (Princeton, NJ, USA) - See all my reviews
(VINE VOICE)   

This review is from: Algebraic Graph Theory (Cambridge Mathematical Library) (Paperback)

This is a very nice book, which gives an introduction to some active areas of current research, but it does not really have too much depth (even in the references), so if you are doing research in this or related subjects, I would recommendSpectra of Graphs, 87: Theory and Application (Pure and Applied Mathematics (Academic Pr)) (yes, it is out of print, and yes, it costs a mint, but your university library probably has it). Godsil's book (referered to in a previous review) is much more algebraic and much less pleasant to read than Biggs.