TY - JOUR

T1 - The maximum Randić index of chemical trees with k pendants

AU - SHIU, Wai Chee

AU - Zhang, Lian zhu

N1 - Funding Information:
This work is partially supported by GRF, Research Grant Council of Hong Kong; FRG, Hong Kong Baptist University; and National Natural Science Foundation of China (No. 10831001).

PY - 2009/7/6

Y1 - 2009/7/6

N2 - 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 frac(n, 2) + frac((3 sqrt(2) + sqrt(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.

AB - 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 frac(n, 2) + frac((3 sqrt(2) + sqrt(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.

KW - Chemical trees

KW - Connectivity index

KW - Randić index

UR - http://www.scopus.com/inward/record.url?scp=67349122632&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2009.01.021

DO - 10.1016/j.disc.2009.01.021

M3 - Article

AN - SCOPUS:67349122632

VL - 309

SP - 4409

EP - 4416

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 13

ER -