Geodesic
A note on Zagreb indices inequality for trees and unicyclic graphs
Ars mathematica contemporanea, Volume 5 (2012) no. 1, pp. 73-76

See the original article notice from the Ars Mathematica Contemporanea website source

For a simple graph G with n vertices and m edges, the inequality M1(G)/n ≤ M2(G)/m, where M1(G) and M2(G) are the first and the second Zagreb indices of G, is known as Zagreb indices inequality. Recently Vukičević and Graovac [VG], and Caporossi, Hansen and Vukčević [CHV] proved that this inequality holds for trees and unicyclic graphs, respectively. Here, alternative and shorter proofs of these results are presented.[VG] D. Vukičević and A. Graovac, Comparing Zagreb M1 and M2 indices for acyclic molecules, MATCH Commun. Math. Comput. Chem. 57 (2007), 587-590.[CHV] G. Caporossi, P. Hansen and D. Vukičević, Comparing Zagreb indices of cyclic graphs, MATCH Commun. Math. Comput. Chem. 63 (2010), 441-451.
DOI: 10.26493/1855-3974.173.9bb
Keywords: First Zagreb index, Second Zagreb index. 
Vesna Andova; Nathann Cohen; Riste Škrekovski. A note on Zagreb indices inequality for trees and unicyclic graphs. Ars mathematica contemporanea, Volume 5 (2012) no. 1, pp. 73-76. doi: 10.26493/1855-3974.173.9bb
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