Weighted zeta functions of graphs

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 -cover of a symmetric digraph for any finite group and g ∈ . 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. © 2002 Elsevier Science Inc. All rights reserved. AMS classification: 05C50; 05C25; 05C10; 15A15; 11F72