A generalized Ihara zeta function formula for simple graphs with bounded degree

TL;DR

This paper extends the Ihara zeta function formula to a broader class of simple graphs with bounded degree, generalizing previous results that were limited to vertex-transitive graphs.

Contribution

The paper introduces a generalized Ihara zeta function formula applicable to simple graphs with bounded degree, expanding the scope beyond vertex-transitive graphs.

Findings

Derived a new formula for the Ihara zeta function for bounded degree graphs

Generalized previous formulas from vertex-transitive to broader graph classes

Provides a theoretical foundation for analyzing spectral properties of bounded degree graphs

Abstract

We establish a generalized Ihara zeta function formula for simple graphs with bounded degree. This is a generalization of the formula obtained by G. Chinta, J. Jorgenson and A. Karlsson from a vertex-transitive graph.