A generalized Bartholdi zeta function for a regular covering of a bipartite graph

Recently, Sato [13] introduced a generalized Bartholdi zeta function of a bipartite graph, and presented three determinant expressions of it.At first, we present a decomposition formula for the generalized Bartholdi zeta function of a regular covering of a bipartite graph G. Furthermore, we introduce a generalized Bartholdi L-function of G, and give three determinant expressions of it. As applications, we present three types of decomposition formulas for the generalized Bartholdi zeta function of a regular covering of G by its generalized Bartholdi L-functions.