A note on Zagreb indices inequality for trees and unicyclic graphs

Vesna Andova, Nathann Cohen, Riste Škrekovski

Abstract


For a simple graph G with n vertices and m edges, the inequality M1(G)/nM2(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.


Keywords


First Zagreb index, Second Zagreb index.

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DOI: https://doi.org/10.26493/1855-3974.173.9bb

ISSN: 1855-3974

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