The maximum Randić index of chemical trees with pendants

A tree is a chemical tree if its maximum degree is at most 4. Hansen and Mélot [P. Hansen, H. Mélot, Variable neighborhood search for extremal graphs 6: analyzing bounds for the connectivity index, J. Chem. Inf. Comput. Sci. 43 (2003) 1–14], Li and Shi [X. Li, Y.T. Shi, Corrections of proofs for Hansen and Mélot’s two theorems, Discrete Appl. Math., 155 (2007) 2365–2370] investigated extremal Randić indices of the chemical trees of order n with k pendants. In their papers, they obtained that an upper bound for Randić index is n 2 + ( 3 2 + 6 − 7 ) k 6 . This upper bound is sharp for n ≥ 3 k − 2 but not for n < 3 k − 2 . In this paper, we find the maximum Randić index for n < 3 k − 2 . Examples of chemical trees corresponding to the maximum Randić indices are also constructed.