Comparability graphs and molecular properties. A novel approach to the ordering of isomers

Abstract

A graph-theoretical approach to the problem of hierarchical ordering of isomeric structures, which is relevant to their properties, has been developed. The key to this approach is the so-called comparability graph which is based on a number of structural rules derived in advance. These rules express the regular change in the different topological indices occurring upon certain systematic changes in the structure of isomeric molecules. They are presented as partial comparability graphs where the vertices correspond to the isomers while the directed edges correspond to the isomer interconversions. The total comparability graph for a complete set of isomers is built by superimposing the partial graphs. The paths on such an oriented graph specify the ordering of vertices. Each path contains comparable isomers which may be regarded as an optimized correlation sample for various structure–property correlations. The isomers from different graph paths are viewed as non-comparable, owing to different alterations in their topology. Such isomers should not be included in the same correlation sample. To illustrate the approach, the importance of the comparability graphs of C₇- and C₈-alkane isomers has been examined with regard to 20 molecular properties.