Algebraic Graph Theory (Cambridge Mathematical Library) 2nd Edition by Norman Biggs (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐I bought this book because I need to look for connections between groups and the graph complement of a graph G. The book is ok but unfottunately I did not find information about the topic I am researching.

⭐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 recommend

⭐(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.

⭐I was using the much more modern standard Godsil & Royle textbook as part of an OU course and was struggling dreadfully. I decided to try this text as it was referred to by most people in the field, and found it so much easier to follow and understand. This is partly because I had limited background in the topic, but also because the style is, for me, less intimidating. It reminded me of a wonderful old school textbook (that I used in the 1960s) which got me through some pretty tough exams , but had been published/printed in 1906!

⭐Puede entenderse para principiantes, pero es formal y muy bueno.

⭐

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