A note on the Kirchhoff index of bicyclic graphs.

Abstract

Resistance distance was introduced by Klein and Randic as a generalization of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices. In this paper, we determine the bicyclic graph of order n ≥ 8 with maximal Kirchhoff index. This improves and extends an earlier result by Zhang et al. [19].