Estimating the connectivity index of a saturated hydrocarbon

Lower and upper bounds for the connectivity index chi of arbitrary saturate d hydrocarbons are obtained. Contrary to the previously known estimates of the same kind (which depend on the Laplacian eigenvalues of the molecular g raph), the new bounds are expressed in terms of two simple structural param eters: number of carbon atoms (n) and number of carbon-carbon bonds (m): (4 n+m)/12 less than or equal to chi less than or equal to>(*) over bar * (3m- 2n)/2+(n-m)root2. Nevertheless, these bounds are, often (but not always) be tter than the earlier ones and are quite sharp. By means of the present est imates, n and m are identified as the parameters determining the gross part of chi. The functional dependence of chi on n and m is essentially linear.