Vertex Degree Weighted Path Indices

Vertex degree weighted path indices P(N)(a, b, ...), for example P(1)(a, b), P(2)(a, b, c), P(3)(a, b, c, d), and P(4)(a, b, c, d, e), are good topological indices for some of the physicochemical properties of octanes with |R|(max) up to 0.999. Mutually optimized combinations of them are even better, R (P(1)..P(4)) is in the worst tested case > 0.9. The best results are obtained in mutually optimized combinations of some of them with some of the elements of the Universal matrix, in the worst tested case R = 0.994. Some of the vertex degree weighted path one indices give rise to a "regular" sequence of octane isomers of increasing branching.