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), 33–46], 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. http://www.imvibl.org/buletin/bulletin_imvi_3_2_2013/bulletin_imvi_3_2_2013_161_164.pdf
