Zeta Functions of Graphs

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.

Author: Audrey Terras
Publisher: Cambridge University Press
Published: 11/18/2010
Pages: 252
Binding Type: Hardcover
Weight: 1.14lbs
Size: 9.10h x 6.10w x 0.60d
ISBN: 9780521113670

Review Citation(s):
Choice 11/01/2011

About the Author
Terras, Audrey: - Audrey Terras is Professor of Mathematics at the University of California, San Diego.