Topological Efficiency of Some Product Graphs

The topological efficiency index of a connected graph G , denoted by ρ(G) is defined as ρ =[2W (G )/ |V (G ) |w(G )] , where w(G ) = min{wv (G ) :v ∈V (G )} and W(G) is the Wiener index of G. In this paper, we obtain the value of topological efficiency index ρ for some composite graphs such as tensor product, strong product, symmetric difference and disjunction of two connected graphs. Further, we have obtained the topological efficiency index for a double graph of a given graph.