Zeta functions of graphs : a stroll through the garden /

Zeta functions of graphs : a stroll through the garden /

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Bibliographic Details
Author / Creator:Terras, Audrey.
Imprint:New York : Cambridge University Press, 2010.
Description:xii, 239 p. ; 24 cm.
Language:English
Series:Cambridge studies in advanced mathematics ; 128
Cambridge studies in advanced mathematics ; 128.
Subject:
Graph theory.
Functions, Zeta.
Functions, Zeta.
Graph theory.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8266513
Hidden Bibliographic Details
ISBN:9780521113670 (hardback)
0521113679 (hardback)
Summary:"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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