Corrections of proofs for Hansen and Mélot's two theorems |
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Authors: | Xueliang Li Yongtang Shi |
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Institution: | Center for Combinatorics and LPMC, Nankai University, Tianjin 300071, PR China |
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Abstract: | The Randi? index R(G) of a (chemical) graph G is also called connectivity index. Hansen and Mélot Variable neighborhood search for extremal graphs 6: analyzing bounds for the connectivity index, J. Chem. Inf. Comput. Sci. 43 (2003) 1-14] in their paper, characterized the chemical trees of given order and number of pendent vertices which have the minimum and maximum Randi? index, respectively. In this note, we point out the mistakes in the proofs of their results Theorems 8 and 10, while we still believe that the two theorems are true, and then we give their corrected proofs. |
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Keywords: | Chemical tree Pendent path Randi? index Connectivity index |
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