Maximum reciprocal degree resistance distance index of unicyclic graphs

Abstract

The reciprocal degree resistance distance index of a connected graph $G$ is defined as $RDR(G)=\sum _{\{u,v\}\subseteq V(G)}\frac{d_G(u)+d_G(v)}{r_G(u,v)}$, where $r_G(u,v)$ is the resistance distance between vertices $u$ and $v$ in $G$. Let ${\mathcal{U}}_n$ denote the set of unicyclic graphs with $n$ vertices. We study the graph with maximum reciprocal degree resistance distance index among all graphs in ${\mathcal{U}}_n$, and characterize the corresponding extremal graph.