Zeta Functions for Images of Graph Coverings by Some Operations

We consider the zeta functions of the line graph and the middle graph of a regular covering of a graph G, and their related topics. Let M (G) be the middle graph of G and T (G) the total graph of G. We show that the middle graph and the total graph of a regular covering of a graph G with covering transformation group A is a regular covering of M (G) and T (G) with the same covering transformation group A, respectively. For a regular graph G, we express the zeta functions of the line graph and the middle graph of a regular covering of G by using the characteristic polynomial of that regular covering.