Let H be a connected graph with vertex and edge sets V(H) and E(H), respectively. As usual, the distance between the vertices u and v of H is denoted by d(u,v) and it is defined as the number of edges in a minimal path connecting the vertices u and v. A topological index is a real number related to a graph. It must be a structural invariant, i.e., it preserves by every graph automorphisms. There are several topological indices have been defined and many of them have found applications as means to model chemical, pharmaceutical and other properties of molecules. The Wiener index W is one of the most studied topological index, see for details [4,5]. It is equal to the sum of distances between all pairs of vertices of the respective graph,[11].
