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: 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. : (htm) : 3916, : 777, : 5. |