Collect. Czech. Chem. Commun. 1990, 55, 630-633

Molecular connectivity indices revisited

Milan Kunz

Chemopetrol, Research Institute of Macromolecular Chemistry, 656 49 Brno


It is shown that the product νiνj of degrees ν of vertices ij, incident with the edge ij, is the number of paths of length 1, 2, and 3 in which the edge is in the center. The unified connectivity index χm = Σ(νiνj)m, where the sum is made over all edges, with m = 1, is the sum of the number of edges, the Platt number and the polarity number. And it is identical with the half sum of the cube A3 of the adjacency matrix A. The Randić index χ-1/2 of regular graphs does not depend on their connectivity.