Comparability graphs and molecular properties: IV. Generalizations and applications

The development of a recently proposed method for calculating molecular properties is outlined. The approach is based on the idea of constructing optimized compound samples for structure—property or structure-activity correlations by means of the so—called comparability graphs (CG) of isomeric compounds. A dynamic comparability principle is devised, proceeding from a series of standard molecular rearrangements described in graph—theoretical terms as rules on molecular branching and cyclicity. An extension of the approach is presented for both the construction of CG's and their combination for variable numbers of atoms. The method is applied to various physico-chemical properties, which are thus divided into three groups according to the degree to which they are conditioned by molecular topology. The Wiener topological index is shown to produce a highly linear correlation with the alkane critical densities and volumes, as well as with their heats and entropies of vaporization.Dedicated to the memory of Professor Oskar E. Polansky, a pioneer of chemical graph theory