Maximum Reciprocal Degree Resistance Distance Index of Bicyclic Graphs

Abstract

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 ℬn 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 ℬn and characterize the corresponding extremal graph.