Vertex degree weighted path indices

Abstract

Vertex degree weighted path indices P_N(a, b, ...), for example P₁(a, b), P₂(a, b, c), P₃(a, b, c, d), and P₄(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 (P₁..P₄) 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.