Abstract

In her Ph.D. Thesis, Czarneski began a preliminary study of the coeficients 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 coeficients. 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.

Keywords

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

Mathematical Subject Classification

Primary: 00A05

Authors