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

Abstract

The reformulated reciprocal product-degree distance of a connected graph G is defined as whe s the degree of vertex u, and v) is the distance between vertices u and v in G. This graph invariant is the generalization of £-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. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.