The maximum Randić index of chemical trees with k pendants

• Published in: Discrete mathematics Vol. 309; no. 13; pp. 4409 - 4416
• Main Authors: Shiu, Wai Chee, Zhang, Lian-zhu
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 06.07.2009; Elsevier
• Subjects: Applied sciences; Chemical trees; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Connectivity index; Exact sciences and technology; Graph theory; Information retrieval. Graph; Mathematics; Randić index; Sciences and techniques of general use; Theoretical computing; Randić index; Chemical trees; Connectivity index; Upper bound; Maximum; Graph connectivity; Proof; Index; Corrections; N order
• ISSN: 0012-365X; 1872-681X
• DOI: 10.1016/j.disc.2009.01.021

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.