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2008 The coefficients of the Ihara zeta function
Geoffrey Scott, Christopher Storm
Involve 1(2): 217-233 (2008). DOI: 10.2140/involve.2008.1.217

Abstract

In her Ph.D. Thesis, Czarneski began a preliminary study of the coefficients of the reciprocal of the Ihara zeta function of a finite graph. We give a survey of the results in this area and then give a complete characterization of the coefficients. As an application, we give a (very poor) bound on the number of Eulerian circuits in a graph. We also use these ideas to compute the zeta function of graphs which are cycles with a single chord. We conclude by posing several questions for future work.

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Geoffrey Scott. Christopher Storm. "The coefficients of the Ihara zeta function." Involve 1 (2) 217 - 233, 2008. https://doi.org/10.2140/involve.2008.1.217

Information

Received: 29 October 2007; Revised: 28 February 2008; Accepted: 6 May 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1228.05202
MathSciNet: MR2429660
Digital Object Identifier: 10.2140/involve.2008.1.217

Subjects:
Primary: 00A05

Keywords: ‎digraph‎ , Eulerian circuit , graph , graph zeta , Ihara zeta , oriented line graph , polynomial coefficient

Rights: Copyright © 2008 Mathematical Sciences Publishers

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