**:** Gutman I.,

Goubko M. V.
**:** Trees with fixed number of pendent vertices with minimal first Zagreb Index

**:**
**:** 2013
** :**
** :** Bulletin of International Mathematical Virtual Institute

** () :** Vol. 3(2)
** :** Gutman I., Goubko M.V. Trees with fixed number of pendent vertices with minimal first Zagreb Index // Bulletin of International Mathematical Virtual Institute, 2013. Vol. 3(2). P. 161-164.

**:** The ﬁrst Zagreb index M1 of a graph G is equal to the sum of squares of the vertex degrees of G. In a recent work [Goubko, MATCH Commun. Math. Comput. Chem. 71 (2014), 3346], it was shown that for a tree with n_1 pendent vertices, the inequality M1 >= 9n_1−16 holds. We now provide an alternative proof of this relation, and characterize the trees for which the equality holds.

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