Type of Document 
Dissertation 
Author 
Czarneski, Debra

URN 
etd07072005121013 
Title 
Zeta Functions of Finite Graphs 
Degree 
Doctor of Philosophy (Ph.D.) 
Department 
Mathematics 
Advisory Committee 
Advisor Name 
Title 
Robert Perlis 
Committee Chair 
Bogdan Oporowski 
Committee Member 
Helena Verrill 
Committee Member 
Lawrence Smolinsky 
Committee Member 
Stephen Shipman 
Committee Member 
Lynn LaMotte 
Dean's Representative 

Keywords 
 zeta function
 spectrum
 biregularbipartite graph
 bipartite graph

Date of Defense 
20050422 
Availability 
unrestricted 
Abstract
Ihara introduced the zeta function of a finite graph in 1966 in the context of padic 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.

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