Molecular topology. IV. Regressive vertex degrees (new graph invariants) and derived topological indices

New local graph invariants, “regressive vertex degrees” (which are slightly augmented vertex degrees) are introduced on the basis of decreasing contributions of more remote vertexes to the classical vertex degrees. Several such invariants are proposed (BR, ER, SR) where t (either t = 1 or t = 2) is an operator expressing the attenuation with increasing topological distance, according to formula (1) or (2). With the aid of these new local invariants, new topological indices (global graph invariants), Y (namely BY, EY or SY) are introduced and exemplified. Their ability to express the branching and to order alkanes is investigated. An appendix gives some recursive relationships for computing these indices.