Note: Corrections of proofs for Hansen and Mélot's two theorems

Authors:
Xueliang Li;Yongtang Shi
Affiliations:
Center for Combinatorics and LPMC, Nankai University, Tianjin 300071, PR China;Center for Combinatorics and LPMC, Nankai University, Tianjin 300071, PR China
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

The Randic index R(G) of a (chemical) graph G is also called connectivity index. Hansen and Melot [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 Randic 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.