On the Reciprocal Degree Distance of Graphs with Cut Vertices or Cut Edges

Abstract

As an additive weight version of the Harary index, the reciprocal degree distance of a simple connected graph $G$ is defined as $RDD(G)=\sum _{u,v\subseteq V(G)}\frac{d_G(u)+d_G(v)}{d_G(u,v)}$, where $d_G(u)$ is the degree of $u$ and $d_G(u,v)$ is the distance between $u$ and $v$ in $G$. In this paper, we respectively characterize the extremal graphs with the maximum $RDD$-value among all the graphs of order $n$ with given number of cut vertices and cut edges. In addition, an upper bound on the reciprocal degree distance in terms of the number of cut edges is provided.