The Ihara expression for generalized weighted zeta functions of Bartholdi type on finite digraphs

TL;DR

This paper derives a unified Ihara expression for a generalized weighted zeta function applicable to finite digraphs, including those with multi-edges and multi-loops, broadening the scope of existing zeta function formulas.

Contribution

It provides a comprehensive Ihara expression that unifies various known zeta functions for finite digraphs, accommodating complex graph structures.

Findings

Unified Ihara expression for generalized weighted zeta functions

Applicable to digraphs with multi-edges and multi-loops

Broadens the theoretical framework for zeta functions in graph theory

Abstract

The Ihara expression of a weighted zeta function for a general finite digraph is given. It unifies all the Ihara expressions obtained for known zeta functions for finite digraphs. Any digraph in this paper permits multi-edges and multi-loops.