Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002



Relations between hyper - Wiener numbers of benzenoid hydrocarbons and phenylenes


Aleksander Vesel1,2 and Igor Pesek1


1 Department of Mathematics, PEF, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia


2 IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia




Topological indices are numerical structure-descriptors deduced from the molecular graph. The hyper-Wiener index WW is one of the recently conceived distance-based graph invariants, used as a structure-descriptor for predicting physico-chemical properties of organic compounds.

Phenylenes are conjugated molecules consisting of condensed 4-membered and 6-membered rings (benzene), in which each 4-membered ring is adjacent to two 6-membered rings, while on the contrary benzene rings are not adjacent to each other.
A catacondensed benzenoid hydrocarbon is associated to a phenylene in a natural manner. Such a benzenoid system was named the "hexagonal squeeze" of the respective phenylene. A phenylene uniquely induces hexagonal squeeze and vice versa.

Gutman and Klavžar, using the method of elementary cut, deduced relations between the Wiener numbers of a phenylene and the catacondensed benzenoid hydrocarbon associated to it (the hexagonal squeeze).

We present the computer program, which randomly generates given number of phenylenes (and their hexagonal squeezes) with fixed (given as an input) number of hexagons. The program computes the hyper-Wiener indices of the phenylenes as well as the hyper-Wiener indices of their hexagonal squeezes.

In order to establish the relations between the hyper-Wiener numbers of a phenylene and their hexagonal squeeze several runs were executed for phenylenes (and their squeezes) with fixed number of hexagons. The results imply strong correlation between the hyper-Wiener numbers of these two classes of molecules.