A Method for Computing Wiener Index with Knowledge of its Szeged Index and Eccentricity Connectivity Index

Let G=(V,E) be a graph of order n and size m. Let W(G) , Sz(G) and eps^c(G) show the Wiener index, the Szeged and eccentricity connectivity indices of G respectively. In this paper, we consider the function beta(G)=W(G)- eps^c(G)and alpha(G)=Sz(G)-W(G) . Then we characterize the trees with minimum value of beta(G) and alpha(G) apply to obtain an upper bound for Wiener index of the general fullerene graphs and an exact formula for a class of dendrimer nanostars. The worth of this method is that it is depended on the structure of blocks in graph and so we can apply it for any kind of chemical graphs.