A note on Zagreb indices inequality for trees and unicyclic graphs
Résumé
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.