ENGLISH

Zeta Functions of Graphs: A Stroll through the Garden

By Audrey Terras

Book information

Publisher
Cambridge University Press
Year
2010
ISBN
0521113679, 9780521113670
LCC
QA166 .T47 2010
Open Library ID
OL24538737M
Language
english
Format
PDF
Filesize
2 MB (2450542 bytes)
Series
Cambridge Studies in Advanced Mathematics 128
Edition
1
Pages
253\253
Time added
2011-01-06 10:13:16

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. Pitched at beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and diagrams, and exercises throughout, theoretical and computer-based.

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