Zeta functions of finite graphs and coverings
type: Item
instance of: scholarly article
title: Zeta functions of finite graphs and coverings
zbMATH Open document ID: 0874.11064
author: Audrey A. Terras
author: Harold M. Stark
published in: Advances in Mathematics
publication date: 1996-11-17T00:00:00Z
review text: This paper deals with zeta functions \(Z_X(u)\) attached to a finite connected, possibly regular, graph \(X\). They originate with a zeta function of Ihara and are generalized by the authors. There are three types of generalizations of zeta functions; zeta functions with vertex variables, zeta functions with edge variables, zeta functions with path variables, the latter appearing here for the first time. The authors show how to specialize the edge variables and the path variables to obtain zeta functions with vertex variables. In addition, they give elementary proofs of Ihara's formula, which says that the zeta function for a regular graph is the reciprocal of a polynomial. Many examples of covering graphs are also considered in this paper.
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11T99
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 934294
zbMATH Keywords: zeta functions of finite graphs
zbMATH Keywords: Ihara zeta-function
zbMATH Keywords: zeta functions with path variables
zbMATH Keywords: edge variables
zbMATH Keywords: vertex variables
zbMATH Keywords: covering graphs
reviewed by: Masakazu Muro
MaRDI profile type: Publication
full work available at URL: aima.1996.0050
OpenAlex ID: W4213281018
DOI: 10.1006/AIMA.1996.0050
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description: scientific article; zbMATH DE number 934294