Ordering of Kekulé structures using nonadjacent numbers

Kekule indices and conjugated circuits are computed for 36 Kekule structures, together with two VB quantities associated with the corresponding factor graphs (previously called submolecules). These latter quantitites are nonadjacent numbers of Hosoya and the reciprocal of the connectivity indices of Randic. It was found that the index of Hosoya successfully orders a set of Kekule structures belonging to the same hydrocarbon in a parallel order as their Kekule indices and branching indices. This substantiates the relation between VB and MO theories. A code is derived by summing contributions of nonadjacent numbers in all Kekule stuctures of a hydrocarbon. The order of the resulting codes is found to be identical to the order of the molecular properties (resonance energies, π-energies, and eigenvalues) of the hydrocarbons.