Reciprocal degree distance and graph properties
The reciprocal degree distance (RDD), defined for a connected graph $G$ as vertex-degree- weighted sum of the reciprocal distances, that is, $\displaystyle{\mathrm{RDD}(G) = \sum_{u\neq v}\frac{d_G(u)+d_G(v)}{d_G (u,v)} }$ , where $d_G(u)$ is the degree of the vertex $u$ in the graph $G$ and $d_G(u,v)$ denotes the distance between two vertices $u$ and $v$ in the graph $G$. In this paper, the authors give sufficient conditions for a graph to be $k$-connected or $\beta$-deficient in terms of the reciprocal degree distance.
scientific article; zbMATH DE number 7040818
scientific article