图的正则覆盖顶点矩阵加权Zeta函数

A Vertex Matrix-Weighted Zeta Function of Regular Coverings of a Graph

本文首先介绍了关于Zeta函数的课题来源及意义,然后介绍了相关研究成果和现状,之后引入了图的顶点矩阵加权的相关定义和定理,再之后给出了图的正则覆盖Zeta函数的行列式表达式及其证明,最后考虑到二部图的特殊性,给出了二部图的覆盖图顶点矩阵加权的Zeta函数。

This paper first introduces the origin and significance of Zeta function, then introduces the related research results and the present situation, and then introduces the related definitions and theorems of vertex matrix weighting of graphs, the determinant expression and its proof of zeta functions of regular covering of a graph are given. At last, considering the particularity of bipartite graphs, the weighted Zeta functions of the vertex matrix of bipartite graphs are given.