Geodesic
On the upper bounds for the first Zagreb index
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 173

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The first Zagreb index $M_1$ is one of the oldest and the most famous topological molecular structure-descriptor, defined as the sum of squares of the degrees of the vertices. In this paper we analyze and compare various upper bounds for the first Zagreb index involving the number of vertices, the number of edges and the maximum and minimum vertex degree. In addition, we propose new upper bound and correct the equality case in [M. Liu, B. Liu, extit{New sharp upper bounds for the first Zagreb index}, MATCH Commun. Math. Comput. Chem. {\bf 62} (2009) 689-698.].
Classification : 05C07 92E10
Keywords: Zagreb index, Vertex degrees, Upper bounds, Chemical graph. 
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Aleksandar Ilić; Milovan Ilić; Bolian Liu. On the upper bounds for the first Zagreb index. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 173 . http://geodesic.mathdoc.fr/item/KJM_2011_35_1_a14/