A note on Zagreb indices inequality for trees and unicyclic graphs

Abstract

For a simple graph G with n vertices and m edges, the inequality M1(G)/n ≤ M1(G)/n; where M 1(G) and M2(G) are the first and the second Zagreb indices of G, is known as Zagreb indices inequality. Recently Vukičević and Graovac [12], and Caporossi, Hansen and Vuki?cević [3] proved that this inequality holds for trees and unicyclic graphs, respectively. Here, alternative and shorter proofs of these results are presented. Copyright © 2012 DMFA Slovenije.