On the multiplicative Wiener index and its possible chemical applications

Ivan Gutman, Wolfgang Linert, István Lukovits, Željko Tomović

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23 Citations (Scopus)


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, Inπ ∼ CW2/3 approaches asymptotically In W, with C being a constant depending on the particular homologous series considered.

Original languageEnglish
Pages (from-to)421-427
Number of pages7
JournalMonatshefte fur Chemie
Issue number5
Publication statusPublished - 1 Jan 2000


  • Chemical graph theory
  • Multiplicative Wiener index
  • Topological index
  • Wiener index


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