Weighted Bartholdi zeta functions of graphs

We define the weighted Bartholdi zeta function of a graph G, and give a determinant expression of it. Furthermore, we define a weighted L-function of G, and present a determinant expression for the weighted L-function of G. As a corollary, we show that the weighted Bartholdi zeta function of a regular covering of G is a product of weighted L-functions of G. © 2005 Elsevier Ltd. All rights reserved.