UID:
edocfu_9959240764102883
Format:
1 online resource (xii, 239 pages) :
,
digital, PDF file(s).
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
Series Statement:
Cambridge studies in advanced mathematics ; 128
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
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
Additional Edition:
ISBN 1-139-63549-2
Additional Edition:
ISBN 0-521-11367-9
Language:
English
