Mathematics Colloquium: Arithmetical Similarities of Graph Coverings

We will explore finite graph coverings from an arithmetical perspective. After discussing how a prime cycle in a graph splits into prime cycles in a covering graph, we will characterize the situation when any prime cycle in a graph has a similar splitting type in two covers. Using this characterization, we present a method of constructing pairs of non-isomorphic graphs that have the same Ihara zeta function.