Zeta Functions of Graphs (Hardcover) (ISBN-13: 9780521113670)

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
ISBN-10: 0521113679
ISBN-13: 9780521113670
Publisher: Cambridge University Press
Language: English
Published: 11/18/2010
Pages: 252
Format: Hardcover
Weight: 1.14lbs
Size: 9.10h x 6.10w x 0.60d

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