A comparison of the Schultz molecular topological index with the Wiener index

The Schultz molecular topological index (MTI) is compared with the Wiener index (W) of a molecular graph. It is shown that 2v(min)W < MTI less than or equal to 4v(max)W holds for any (connected) graph Gamma, with v(min) and v(max) denoting the smallest and the largest valency, respectively, of the vertices of Gamma. For molecular graphs these bounds can be further improved. For instance, for benzenoid systems we have the following: 4W < MTI < 6.93W. This implies that W and MTI are linearly correlated not only in the case of acyclic molecules (which is a previously known result) bur also in the case of molecules with arbitrarily many cycles.