On the multiplicative Wiener index and its possible chemical applications

The recently introduced multiplicative Wiener index pi is a molecular struc ture descriptor equal to the product of the distances between all pairs of vertices of the underlying molecular graph. It was expected that pi has a d ifferent structure dependency than the ordinary Wiener index W which is equ al to the sum of vertex distances. We now show that this is not the case: f or a variety of classes of isomeric alkanes, monocycloalkanes, bicycloalkan es, benzenoid hydrocarbons, and phenylenes a very good (either linear or sl ightly curvilinear) correlation between pi and W is found. For homologous s eries, the relation between pi and W happens to be somewhat less simple. Fo r alkanes, In pi similar to CW2/3 approaches asymptotically In W, with C be ing a constant depending on the particular homologous series considered.