Extremal unicyclic graphs with respect to the reformulated reciprocal product-degree distance

The reformulated reciprocal product-degree distance of a connected graph G is defined as RDDxt = RDDxt (G) = Sigma({u,v}subset of V(G) u not equal v) delta(G)(u)delta(G)(v)/d(G)(u,v) + t, t >= 0, where delta(G)(u) is the degree of vertex u, and d(G)(u, v) is the distance between vertices u and v in G. This graph invariant is the generalization of t-Harary index [K. C. Das, K. Xu, I. N. Cangul, A. S. Cevik, A. Graovac, On the Harary index of graph operations, J. Inequal. Appl. 16 (2013) 2013-339.] and reciprocal product-degree distance [Y. Alizadeh, A. Iranmanesh, T. Doslic, Additively weighted Harary index of some composite graphs, Discrete Math. 313 (2013) 26-34], respectively. In this paper, we determine completely the extremal graph among all unicyclic graphs with n vertices in terms of the reformulated reciprocal product-degree distance.