Zeta functions of graphs : a stroll through the garden / Audrey Terras.

Format:

Book

Author/Creator:

Terras, Audrey, author.

Series:

Cambridge studies in advanced mathematics ; 128.

Cambridge studies in advanced mathematics ; 128

Language:

English

Subjects (All):

Graph theory.

Functions, Zeta.

Physical Description:

1 online resource (xii, 239 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2011.

Summary:

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.

Contents:

Cover; Half-title; Series-title; Title; Copyright; Contents; Illustrations; Preface; I A quick look at various zeta functions; II Ihara zeta function and the graph theory prime number theorem; III Edge and path zeta functions; IV Finite unramified Galois coverings of connected graphs; V Last look at the garden; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-21268-5

0-511-76042-6

1-282-90798-0

9786612907982

0-511-91770-8

0-511-91672-8

0-511-91868-2

0-511-91491-1

0-511-91311-7

OCLC:

689996475