Zeta functions of graphs and coverings

图和覆盖层的 Zeta 函数

基本信息

批准号：
15540147
负责人：
SATO Iwao
金额：
$ 1.15万
依托单位：
Oyama National College of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540147/
关键词：
graph covering zeta function 被膜グラフ

项目摘要

We express an L-function of a regular covering of a graph G by using that of G. Moreover, we treat zeta functions and L-functions of a semiregular bipartite graph, its line graph, its middle graph and their regular coverings, and present an analogue of the Selberg trace formula for an L-function of a semiregular bipartite graph.We consider weighted zeta functions and L-functions of digraphs, and give their determinant expressions. Moreover, we present determinant expressions for weighted zeta functions and weighted L-functions of graphs, and express the weighted zeta function of a regular covering of a graph as a product of its weighted L-functions. By using a similar method to the above one, we present determinant expressions for the weighted complexities of a graph and its (regular or irregular) covering. Furthermore, we present a new decomposition formula for the weighted zeta function of a (regular or irregular) covering of a graph, and study the structure of a balanced covering of a unbalanced graph as an application.Finally, we consider the Bartholdi zeta functions and Bartholdi L-functions of a graph, a digraph and their covering, and present their determinant expressions and decomposition formulas. Furthermore, we present decomposition formulas for the Bartholdi zeta function of some branched covering of a graph, and the weighted Bartholdi zeta function of a graph.

我们通过使用G来表达图形g的定期覆盖g的功能。此外，我们处理半毛的两分图的zeta函数和l功能，其界限，中间图和常规覆盖物，并呈现Selberg痕量的类似物，以用于selebartiate themiregular bipartitions的l函数和ZERICTION ZERICTIONS。决定性表达式。此外，我们提出了图形加权Zeta函数和加权L功能的决定符表达式，并表达图形的常规覆盖物的加权Zeta函数，作为其加权L功能的产物。通过使用与上述类似的方法，我们提出了图形及其（规则或不规则）覆盖的加权复杂性的决定符表达式。此外，我们提出了一个新的分解公式，用于图形覆盖的（规则或不规则）的加权Zeta功能，并研究不平衡图的平衡覆盖的结构作为应用程序。在本文上，我们考虑Bartholdi Zeta Zeta Zeta函数和图形的bartholdi lignaldi＆Bartholdi l-Bartholdi l-Bartholdi ligntions a Graph的功能，图形和封面和他们的封面和确定性和确定性的确定性和确定性。此外，我们提出了一些图的某些分支覆盖物的Bartholdi Zeta功能的分解公式，以及图形的加权Bartholdi Zeta函数。