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Zeta Functions of Graphs

A Stroll through the Garden

Audrey Terras author

Format:Hardback

Publisher:Cambridge University Press

Published:18th Nov '10

Currently unavailable, and unfortunately no date known when it will be back

Zeta Functions of Graphs cover

Combinatorics meets number theory in this stimulating stroll through the zetas. Includes well-chosen illustrations and exercises, both theoretical and computer-based.

This stimulating introduction to zeta (and related) functions of graphs develops the fruitful analogy between combinatorics and number theory - for example, the Riemann hypothesis for graphs - making connections with quantum chaos, random matrix theory, and computer science. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.

'The book is very appealing through its informal style and the variety of topics covered and may be considered the standard reference book in this field.' Zentralblatt MATH

ISBN: 9780521113670

Dimensions: 235mm x 157mm x 19mm

Weight: 530g

252 pages