**:** Goubko M.,

Magnant C.,

Salehi Nowbandegani P.,

Gutman I.
**:** ABC Index of Trees with Fixed Number of Leaves

**:**
** ( ):** Kraguevac University

**:** 2015
** :** ..

** :** MATCH Commun. Math. Comput. Chem.

** () :** 74 (3)
** :** 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.

**:** 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.

At publisher's site
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