Upgrading the Wiener Index

CASTRO, E.A.; GUTMAN, I.; MARINO, D.J.G.; PERUZZO, P. J.

JOURNAL OF THE SERBIAN CHEMICAL SOCIETY

SERBIAN CHEMICAL SOC

Año: 2002 vol. 67 p. 647 - 651

0352-5139

Abstract: TheWiener indexWis the oldest molecular-graph-based structure-descriptor. It is defined as the sum of the distances of all pairs of vertices of the molecular graph G, where the distance is the number of edges in the shortest path connecting the respective vertices, and where G is the hydrogen-depleted molecular graph. This seemingly very simple topological index could be "upgraded" (a) by using as the distance the sum of the bond lengths along the shortest path, or (b) by using the Euclidean distance between the respective pairs of atoms. Each of these "upgraded"Wiener indices could be computed either (
) for the hydrogen-depleted or () for the hydrogen-filled molecular graph.We provide examples showing that none of the modifications (a
), (a), (b
), (b) yields better results than the ordinary Wiener index, and that there is a very good linear correlation betweenWand its "upgraded" variants