Topological Efficiency of Some Product Graphs

Abstract

The topological efficiency index of a connected graph $G,$ denoted by $rho (G),$ is defined as $rho(G)=frac{2W(G)}{left|V(G)right|underline w(G)},$ where $underline w(G)=text { min }left{w_v(G):vin V(G)right}$ and $W(G)$ is the Wiener index of $G.$ In this paper, we obtain the value of topological efficiency index 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.