Distance indices and their hyper-counterparts: intercorrelation and use in the structure-property modeling

Intercorrelation between the Wiener index, hyper-Wiener index, Harary index, hyper-Harary index, detour index and hyper-detour index is studied on three sets of branched and unbranched alkanes and cycloalkanes with up to eight carbon atoms. First set (S-39) contains all alkanes from ethane to octane (39 molecules), the second set (S-139) 139 cyclic hydrocarbons from cyclopropane to branched and unbranched polycyclic octanes and the third set (S-178) is a combination of the first two sets (178 molecules). It is found that the pairs of distance indices and the corresponding hyper-counterparts are highly intercorrelated for all three sets. The use of the distance indices of both kinds in structure-boiling point modeling was analyzed. Distance indices and hyper-distance indices do not lead to particularly good models for any of the three sets. When used as composite indices they give much-improved models. However, they are most useful when combined with such indices as the number of carbon atoms in a hydrocarbon, Hosoya Z index and/or total walk count index. The following standard errors of estimate are obtained for the best models based on the combination of descriptors: 2.1 degrees C (S-39), 4.4 degrees C (S-139) and 4.1 degrees C (S-178). They compare favorably with the related models in the literature.