Summary.
The recently introduced multiplicative Wiener index π is a molecular structure descriptor equal to the product of the distances between all pairs of vertices of the underlying molecular graph. It was expected that π has a different structure dependency than the ordinary Wiener index W which is equal to the sum of vertex distances. We now show that this is not the case: for a variety of classes of isomeric alkanes, monocycloalkanes, bicycloalkanes, benzenoid hydrocarbons, and phenylenes a very good (either linear or slightly curvilinear) correlation between π and W is found. For homologous series, the relation between π and W happens to be somewhat less simple. For alkanes, approaches asymptotically ln W, with C being a constant depending on the particular homologous series considered.
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Received November 24, 1999. Accepted January 11, 2000
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Gutman, I., Linert, W., Lukovits, I. et al. On the Multiplicative Wiener Index and Its Possible Chemical Applications. Monatshefte für Chemie 131, 421–427 (2000). https://doi.org/10.1007/PL00010312
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DOI: https://doi.org/10.1007/PL00010312