Maximum reciprocal degree resistance distance index of bicyclic graphs (Q2045361)

Summary: The reciprocal degree resistance distance index of a connected graph \(G\) is defined as \(\mathrm{RDR}(G)=\sum_{\{u,v\} \subseteq V(G)} ((\mathrm{d}_G (u) + \mathrm{d}_G (v)) / r_G (u,v))\), where \(r_G(u,v)\) is the resistance distance between vertices \(u\) and \(v\) in \(G\). Let \(\mathscr{B}_n\) denote the set of bicyclic graphs without common edges and with \(n\) vertices. We study the graph with the maximum reciprocal degree resistance distance index among all graphs in \(\mathscr{B}_n\) and characterize the corresponding extremal graph.