Reciprocal Degree Distance of Eliasi-Taeri Sums of Graphs

Abstract

For a connected graph G , the reciprocal degree distance is defined as RDD ( G ) = (cid:80) u,v ∈ V ( G ) (cid:0) d G ( u ) + d G ( v ) (cid:1)(cid:0) 2 d G ( u, v ) (cid:1) − 1 , where d G ( u ) denotes the degree of a vertex u in G and d G ( u, v ) represents the distance between the vertices u and v in G . In this paper, upper bounds for the reciprocal degree distance of graphs, arising from four operations introduced by Eliasi and Taeri in [ Discrete Appl. Math. 157 (2009) 794–803], are provided.