Properties Determined by the Ihara Zeta Function of a Graph

Abstract

In this paper, we show how to determine several properties of a finite graph G from its Ihara zeta function ZG(u). If G is connected and has minimal degree at least 2, we show how to calculate the number of vertices of G. To do so we use a result of Bass, and in the case that G is nonbipartite, we give an elementary proof of Bass’ result. We further show… (More)

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