The partial differential coefficients for the second weighted Bartholdi zeta function of a graph

摘要

We consider the second weighted Bartholdi zeta function of a graph G, and present weighted versions for the results of Li and Hou's on the partial derivatives of the determinant part in the determinant expression of the Bartholdi zeta function of G. Furthermore, we give a formula for the weighted Kirchhoff index of a regular covering of G in terms of that of G. (C) 2019 Elsevier B.V. All rights reserved.