Estimating the connectivity index of a saturated hydrocarbon

Abstract

Lower and upper bounds for the connectivity index <img src='/image/spc_char/lembda.gif' border=0> of arbitrary saturated hydrocarbons are obtained. Contrary to the previously known estimates of the same kind (which depend on the Laplacian eigenvalues of the molecular graph), the new bounds are expressed in terms of two simple structural parameters: number of carbon atoms (<i>n</i>) and number of carbon-carbon bonds (<i>m</i>): (<i>4n+m</i>)<i>/</i>12≤<img src='/image/spc_char/lembda.gif' border=0>≤ (3<i>m</i>-2<i>n</i>)/2+ (<i>n-m</i>)<i> √</i>2<i>. </i>Nevertheless, these bounds are often (but not always) better than the earlier ones and are quite sharp. By means of the present estimates, <i>n and m</i> are identified as the parameters determining the gross part of <img src='/image/spc_char/lembda.gif' border=0>· The functional dependence of <img src='/image/spc_char/lembda.gif' border=0> on <i>n </i>and <i>m </i>is essentially linear.