Zeta Functions of Graphs: A Stroll through the Garden: 128 (Cambridge Studies in Advanced Mathematics, Series Number 128) - Image 1

£59.82

Cambridge University Press Zeta Functions of Graphs: A Stroll through the Garden: 128 (Cambridge Studies in Advanced Mathematics, Series Number 128)

Name: Zeta Functions of Graphs: A Stroll through the Garden: 128 (Cambridge Studies in Advanced Mathematics, Series Number 128)
Brand: Cambridge University Press
Price: 59.82 GBP
Availability: InStock

Combinatorics & Graph Theory

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Description

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.

Product Specifications

Brand: Cambridge University Press
Format: hardcover
ASIN: 0521113679
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Combinatorics & Graph Theory
Domain: Amazon UK
Release Date: 18 November 2010
Listed Since: 19 March 2010

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Cambridge University Press Zeta Functions of Graphs: A Stroll through the Garden: 128 (Cambridge Studies in Advanced Mathematics, Series Number 128)

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