For a saturated hydrocarbon with n carbon atoms and m carbon-carbon bonds a
nd with Randic connectivity index chi, two functions, L = L(n,m) and U = U(
n,m), are determined, such that L less than or equal to chi less than or eq
ual to U. These bounds are better than those previously reported; for most
chemically relevant values of n and m there exist hydrocarbons for which ch
i = L or chi = U.