A new generalized Bartholdi zeta function for a digraph

We define a new generalized Bartholdi zeta function of a digraph D, and give a determinant expression of it. We present a decomposition formula for the new generalized Bartholdi zeta function of a group covering of D. Furthermore, we introduce a new generalized Bartholdi L-function of D, and give a determinant expressions of it. As an application, we present a decomposition formula for the new generalized Bartholdi zeta function of a group covering of D by its new generalized Bartholdi L-functions.

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