Zeta Functions of Graphs

Zeta Functions of Graphs
Author: Audrey Terras
Publisher: Cambridge University Press
Total Pages: 253
Release: 2010-11-18
Genre: Mathematics
ISBN: 1139491784


Download Zeta Functions of Graphs Book in PDF, Epub and Kindle

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.


Zeta Functions of Graphs
Language: en
Pages: 253
Authors: Audrey Terras
Categories: Mathematics
Type: BOOK - Published: 2010-11-18 - Publisher: Cambridge University Press

GET EBOOK

Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables.
Zeta Functions of Graphs
Language: en
Pages: 252
Authors: Audrey Terras
Categories: Electronic book
Type: BOOK - Published: 2010 - Publisher:

GET EBOOK

Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables.
Ihara Zeta Functions of Irregular Graphs
Language: en
Pages: 93
Authors: Matthew D. Horton
Categories:
Type: BOOK - Published: 2006 - Publisher:

GET EBOOK

We explore three seemingly disparate but related avenues of inquiry: expanding what is known about the properties of the poles of the Ihara zeta function, deter
Emerging Applications of Number Theory
Language: en
Pages: 693
Authors: Dennis A. Hejhal
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increa
Zeta Functions of Finite Graphs
Language: en
Pages:
Authors: Debra Czarneski
Categories:
Type: BOOK - Published: 2005 - Publisher:

GET EBOOK