Edge Zeta Functions of Graph Coverings

Abstract

We give a decomposition formula for the edge zeta function of a regular covering \(\overrightarrow{G}\) of a graph \(G\). Furthermore, we present a determinant expression for some \(Z\)-function of an oriented line graph \(\overrightarrow{L}(G)\) of \(G\). As a corollary, we obtain a factorization formula for the edge zeta function of \(\overrightarrow{G}\) by \(L\)-functions of \(\overrightarrow{L}(G)\).