非正则覆盖图的加权Zeta函数

Weighted Zeta Functions of Irregular Graphs

本文主要研究非正则覆盖图的加权zeta函数的基本性质。Ihara和Sato研究了正则覆盖图的加权zeta函数的行列式表示和极点分布,本文的主要目的就是将正则覆盖图推广到非正则覆盖图的形式,讨论非正则覆盖图的加权zeta函数的分解为zeta函数的乘积的形式以及不同的非正则覆盖图的加权zeta函数之间的联系。

In this paper, we will mainly research on the basic properties of weighted zeta functions of irregular covering of graphs. Ihara and Sato had major researched on the determinant expressions and boundary of the poles of the weighted zeta functions of regular covering of graphs. The major point of this paper is extending to the irregular of graphs. We will present a factorization of the weighted zeta function of an irregular covering of graph by a series of zeta functions and the relationship between different weighted zeta functions of irregular covering of graphs.