Weighted zeta functions of digraphs

AbstractWe define a weighted zeta function of a digraph and a weighted L-function of a symmetric digraph, and give determinant expressions of them. Furthermore, we give a decomposition formula for the weighted zeta function of a g-cyclic Γ-cover of a symmetric digraph for any finite group Γ and g∈Γ.A decomposition formula for the weighted zeta function of an oriented line graph L→(G̃) of a regular covering G̃ of a graph G is given. Furthermore, we define a weighted L-function of an oriented line graph L→(G) of G, and present a factorization formula for the weighted zeta function of L→(G̃) by weighted L-functions of L→(G). As a corollay, we obtain a factorization formula for the multiedge zeta function of G̃ given by Stark and Terras