Graph Classes (Dis)satisfying the Zagreb Indices Inequality - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue MATCH Communications in Mathematical and in Computer Chemistry Année : 2011

Graph Classes (Dis)satisfying the Zagreb Indices Inequality

Résumé

{Recently Hansen and Vukicevic proved that the inequality $M_1/n \leq M_2/m$, where $M_1$ and $M_2$ are the first and second Zagreb indices, holds for chemical graphs, and Vukicevic and Graovac proved that this also holds for trees. In both works is given a distinct counterexample for which this inequality is false in general. Here, we present some classes of graphs with prescribed degrees, that satisfy $M_1/n \leq M_2/m$: Namely every graph $G$ whose degrees of vertices are in the interval $[c; c + \sqrt c]$ for some integer $c$ satisies this inequality. In addition, we prove that for any $\Delta \geq 5$, there is an infinite family of graphs of maximum degree $\Delta$ such that the inequality is false. Moreover, an alternative and slightly shorter proof for trees is presented, as well\ as for unicyclic graphs.
Fichier principal
Vignette du fichier
01108.pdf (155.06 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00531290 , version 1 (02-11-2010)

Identifiants

  • HAL Id : hal-00531290 , version 1

Citer

Vesna Andova, Nathann Cohen, Riste Skrekovski. Graph Classes (Dis)satisfying the Zagreb Indices Inequality. MATCH Communications in Mathematical and in Computer Chemistry, 2011, 65 (3), pp.647-658. ⟨hal-00531290⟩
719 Consultations
128 Téléchargements

Partager

Gmail Facebook X LinkedIn More