Collection of Czechoslovak Chemical Communications - digital archive 

Abstract

It is shown that the product ν_iν_j 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 χ_m = Σ(ν_iν_j)^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.