**:** Goubko M. V.,

Reti T.
**:** Note on Minimizing Degree-Based Topological Indices of Trees with Given Number of Pendent Vertices

**:**
**:** 2014
** :** ..

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

** () :** V. 72, No 3
** :** M. Goubko, T. Reti. Note on Minimizing Degree-Based Topological Indices of Trees with Given Number of Pendent Vertices // MATCH Commun. Math. Comput. Chem. 2014. V. 72, No 3. pp. 633-639.

**:** Theorem 3 in [Goubko M. Minimizing Degree-Based Topological Indices for Trees with Given Number of Pendent Vertices // MATCH Commun. Math. Comput. Chem. 2014. V. 71, No 1. P. 33-46.] claims that the second Zagreb index M2 cannot be less than 11n - 27 for a tree with n >= 8 pendent vertices. Yet, a tree exists with n = 8 vertices (the two-sided broom) violating this inequality. The reason is that the proof of Theorem 3 relays on a tacit assumption that an index-minimizing tree contains no vertices of degree 2. This assumption appears to be invalid in general. In this note we show that the inequality M2 >= 11n-27 still holds for trees with n >= 9 vertices and provide the valid proof of the (corrected) Theorem 3.

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