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The reciprocal degree resistance distance index of a connected graph G is defined as RDRG=∑u,v⊆VGdGu+dGv/rGu,v, where rGu,v is the resistance distance between vertices u and v in G. Let Un denote the set of unicyclic graphs with n vertices. We study the graph with maximum reciprocal degree resistance distance index among all graphs in Un and characterize the corresponding extremal graph.

The hyper-Wiener index WW(G) is defined as with the summation going over all pairs of vertices in G. In this paper, we determine graphs with the minimum hyper-Wiener index among all the unicyclic graphs with n vertices and k pendent vertices.