Weighted zeta functions of digraphs Original Research Article

We 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 gset membership, variantΓ. A decomposition formula for the weighted zeta function of an oriented line graph image of a regular covering image of a graph G is given. Furthermore, we define a weighted L-function of an oriented line graph image of G, and present a factorization formula for the weighted zeta function of image by weighted L-functions of image . As a corollay, we obtain a factorization formula for the multiedge zeta function of image given by Stark and Terras.