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 $\overrightarrow{L}(G)$.