Zeta functions from graphs

Zeta functions from graphs

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The location of the nontrivial poles of a generalized zeta function is derived from the spectrum of Ramanujan graphs and bounds are established for irregular graphs. The existence of a similarity transformation of the diagonal matrix given by a specified set of eigenvalues to an adjacency matrix of...

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Bibliographic Details
Main Author: Simon Davis
Format: Article
Language:English
Published: Taylor & Francis Group 2018-08-01
Series:AKCE International Journal of Graphs and Combinatorics
Subjects:
graph
zeta function
adjacency matrix
eigenvalues
Online Access:http://dx.doi.org/10.1016/j.akcej.2017.09.007
Description
Summary:The location of the nontrivial poles of a generalized zeta function is derived from the spectrum of Ramanujan graphs and bounds are established for irregular graphs. The existence of a similarity transformation of the diagonal matrix given by a specified set of eigenvalues to an adjacency matrix of a graph is proven, and the method yields a set of finite graphs with eigenvalues determined approximately by a finite subset of the poles of the Ihara zeta function.
ISSN:0972-8600

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