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Zeta Functions on Kronecker Products of Graphs

Abstract. Ihara introduced the zeta function of a p-adic matrix group in 1966 and the idea was extended to finite graphs by Hashimoto in 1989. In her dissertation, Debra Czarneski explores the properties of graphs that are or are not determined by the zeta function. This paper defines a Kronecker product of finite graphs and explores the question: given a pair of graphs with equal zeta functions, if we take their Kronecker product with a third graph, is the equality of the zeta function preserved?