Abstract: MATH/CHEM/COMP 2002, Dubrovnik,
June 2429, 2002

Relations between
hyper  Wiener numbers of benzenoid hydrocarbons and phenylenes
Aleksander Vesel^{1,2} and Igor Pesek^{1}
^{1 }Department of Mathematics, PEF, University of Maribor, Koroška
cesta 160, SI2000 Maribor, Slovenia ^{2 }IMFM, Jadranska 19, SI1000 Ljubljana, Slovenia Topological indices are numerical structuredescriptors deduced from the molecular graph. The hyperWiener index WW is one of the recently conceived distancebased graph invariants, used as a structuredescriptor for predicting physicochemical properties of organic compounds. Phenylenes are conjugated molecules consisting of
condensed 4membered and 6membered rings (benzene), in which each 4membered
ring is adjacent to two 6membered rings, while on the contrary benzene rings
are not adjacent to each other. 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 hyperWiener indices of the phenylenes as well as the hyperWiener indices of their hexagonal squeezes. In order to establish the relations between the hyperWiener 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 hyperWiener numbers of these two classes of molecules. 