Zeta Functions of Graphs - A Stroll through the Garden (Hardcover)

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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	Cambridge Studies in Advanced Mathematics
Release date:	November 2010
First published:	November 2010
Authors:	Audrey Terras
Dimensions:	235 x 157 x 19mm (L x W x T)
Format:	Hardcover
Pages:	252
ISBN-13:	978-0-521-11367-0
Categories:	Books > Science & Mathematics > Mathematics > Mathematical foundations > General
LSN:	0-521-11367-9
Barcode:	9780521113670

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