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Research Article

The Multiplicative Version of the Wiener Index

Ivan Gutman,^† Wolfgang Linert,^‡ István Lukovits,*^§ and Željko Tomović^†

Faculty of Science, University of Kragujevac, P.O. Box 60, YU-34000 Kragujevac, Yugoslavia, Technical University of Vienna, A-1060 Wien, Getreidemarkt 9, Austria, and Chemical Research Center, Hungarian Academy of Sciences, P.O. Box 17, H-1525 Budapest, Hungary

J. Chem. Inf. Comput. Sci., 2000, 40 (1), pp 113–116

DOI: 10.1021/ci990060s

Publication Date (Web): November 19, 1999

†

University of Kragujevac.

‡

Technical University of Vienna.

Author to whom correspondence should be addressed. Telephone: (36-1) 325-7900. E-mail: lukovits@cric.chemres.hu.

Hungarian Academy of Sciences.

Abstract

The classical Wiener index, W(G), is equal to the sum of the distances between all pairs of vertexes of a (molecular) graph, G. We now consider a related topological index, π(G), equal to the product of distances between all pairs of vertexes of G. The basic properties of the π index are established and its possible physicochemical applications examined. In the case of alkanes, π and W are highly correlated; a slightly curvilinear correlation exists between ln π and W.

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