Graph valence shells as molecular descriptors

We have introduced a new simple structural descriptor for molecules that is based on the count of the valence shells for vertices in molecular graphs. The construction of the new descriptor is illustrated on 2,3-dimethylhexane and is reported for the 18 octane isomers. The relationship of the new descriptor to the path numbers of a graph is discussed. It can be seen that the path counts and the count of valence of neighbor shells are related for paths of length two (and shells of range two). There is no appreciable correlation between the count of the longer paths and the count of the corresponding neighbor valence shells at larger separations. Use of the neighbor valence shells as molecular descriptors is illustrated on the boiling point, the entropy, and the density of octanes. An intriguing situation is observed for regressions involving considered properties of n-octane isomers C8H18 in that the paths of length two, three, and four and the shells of the range two, three, and four give identical multivariate regression statistics. An explanation for this somewhat unusual aspect of MRA (multiple regression analysis) is offered.