TOPOLOGICAL ORDER IN MOLECULES .1. MOLECULAR BRANCHING REVISITED

The development of the idea of molecular branching is reviewed from the first topological indices used to quantify the branching of the molecular skeleton, to the branching rules derived from different graph invariants, and the topological transferability graphs which place in order all alkanes in paths of increasing branching. It is shown that the topological order thus induced matches to a very high extent the patterns in alkane molecular properties and provides the basis for their reliable calculation and prediction. Generalized branching rules are defined from new formulas for the decrease in the Wiener number and the increase in the number of self-returning walks of degree four upon transformations that increase branching.