Identifier
etd-07072005-121013
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
Ihara introduced the zeta function of a finite graph in 1966 in the context of p-adic matrix groups. The idea was generalized to all finite graphs in 1989 by Hashimoto. We will introduce the zeta function from both perspectives and show the equivalence of both forms. We will discuss several properties of finite graphs that are determined by the zeta function and show by counterexample several properties of finite graphs that are not determined by the zeta function. We will also discuss the relationship between the zeta function of a finite graph and the spectrum of a finite graph.
Date
2005
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Czarneski, Debra, "Zeta functions of finite graphs" (2005). LSU Doctoral Dissertations. 1814.
https://repository.lsu.edu/gradschool_dissertations/1814
Committee Chair
Robert Perlis
DOI
10.31390/gradschool_dissertations.1814