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 - Journal article
AN - SCOPUS:67349122632
SN - 0012-365X
VL - 309
SP - 4409
EP - 4416
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 13
ER -