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Zeta Functions of Graphs (Cambridge Studies in Advanced Mathematics #128) (Hardcover)

Zeta Functions of Graphs (Cambridge Studies in Advanced Mathematics #128) Cover Image
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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.

Product Details
ISBN: 9780521113670
ISBN-10: 0521113679
Publisher: Cambridge University Press
Publication Date: November 18th, 2010
Pages: 252
Language: English
Series: Cambridge Studies in Advanced Mathematics