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јвтор:  Goubko M., Magnant C., Salehi Nowbandegani P., Gutman I.
Ќазвание:  ABC Index of Trees with Fixed Number of Leaves
—татус:  опубликовано
»здательство (дл€ книг и брошюр):  Kraguevac University
√од:  2015
“ип публикации:  стать€ вед.журн.
Ќазвание журнала или конференции:  MATCH Commun. Math. Comput. Chem.
Ќомер (том) журнала:  74 (3)
ѕолна€ библиографическа€ ссылка:  M. Goubko, C. Magnant, P. Salehi Nowbandegani, I. Gutman. ABC Index of Trees with Fixed Number of Leaves, MATCH Commun. Math. Comput. Chem., V. 74, No 3. P. 697-701.
јннотаци€:  Given a graph G, the atom-bond connectivity (ABC) index is defined to be $ABC(G) = \sum_{uv\in E(G)} \sqrt{ \frac{ d_G(u) + d_G(v) - 2 }{d_G(u) d_G(v)} }$, where E(G) is the edge set of graph G and $d_G(v)$ is the degree of vertex v in graph G. The paper [C. Magnant, P. Salehi Nowbandegani, I. Gutman. Which tree has the smallest ABC index among trees with k leaves? Discrete Appl. Math., In Press.] claims to classify those trees with a fixed number of leaves which minimize the ABC index. Unfortunately, there is a gap in the proof leading to other examples that contradict the main result of that work. These examples and the problem are discussed in this work.

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