Title page for ETD etd-07072005-121013

Type of Document Dissertation
Author Czarneski, Debra
URN etd-07072005-121013
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
  • zeta function
  • spectrum
  • biregular-bipartite graph
  • bipartite graph
Date of Defense 2005-04-22
Availability unrestricted
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.
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