The Minimal Kirchhoff Index of Graphs with a Given Number of Cut Vertices

Abstract

The resistance distance was introduced by Klein and Randi´c as a generalization of the classical distance. The Kirchhoff index Kf (G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this paper we determine the extremal graphs with minimal Kirchhoff index among all n-vertex graphs with k cut vertices where $1\leq k< \frac{n}{2}$.