Zeta Functions of Graphs

English

Series: Cambridge Studies in Advanced Mathematics Ser.

ISBN: 0511911149

EAN: 9780511911149

Category: Mathematics / Graphic Methods/Mathematics / Functional Analysis/

Publisher: Cambridge University Press

Release Date: 11/18/2010

Synopsis: 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.

Excerpt: Unknown Property Excerpt

Zeta Functions of Graphs

Illustrated: No

Format: eBook - PDF

Pages: 252