A new determinant expression for the weighted Bartholdi zeta function of a digraph

Abstract

We consider the weighted Bartholdi zeta function of a digraph D, and give a new determinant expression of it. Furthermore, we treat a weighted L-function of D, and give a new determinant expression of it. As a corollary, we present determinant expressions for the Bartholdi edge zeta functions of a graph and a digraph.