Comptes Rendus
no. 9-10
Combinatorics
Some notes on domination edge critical graphs
[Quelques remarques sur les graphes à domination critique par addition dʼarête]

Présenté par : the Editorial Board

Nader Jafari Rad1 ; Sayyed Heidar Jafari1
1 Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 485-488.

Un graphe G est un graphe à domination critique par addition dʼarête, ou simplement γ-critique par arête, si pour toute arête e qui nʼest pas dans G on a γ(G+e)<γ(G). Nous caractérisons les graphes cactus, connexes et γ-critiques par arête.

A graph G is domination edge critical, or just γ-edge critical, if for any edge e not in G, γ(G+e)<γ(G). We will characterize all connected γ-edge critical cactus graphs.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.04.005
Nader Jafari Rad 1 ; Sayyed Heidar Jafari 1

1 Department of Mathematics, Shahrood University of Technology, Shahrood, Iran 
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Nader Jafari Rad; Sayyed Heidar Jafari. Some notes on domination edge critical graphs. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 485-488. doi : 10.1016/j.crma.2011.04.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.04.005/

[1] N. Ananchuen; M.D. Plummer Some results related to toughness of 3-domination critical graphs, Discrete Mathematics, Volume 272 (2003), pp. 5-15

[2] N. Ananchuen; M.D. Plummer Matching properties in domination critical graphs, Discrete Mathematics, Volume 277 (2004), pp. 1-13

[3] O. Favaron; D.P. Sumner; E. Wojcicka The diameter of domination k-critical graphs, Journal of Graph Theory, Volume 18 (1994), pp. 723-734

[4] Fundamentals of Domination in Graphs (T.W. Haynes; S.T. Hedetniemi; P.J. Slater, eds.), Marcel Dekker, Inc., New York, 1998

[5] D. Sumner; P. Blitch Domination critical graphs, Journal of Combinatorial Theory Ser. B, Volume 34 (1983), pp. 65-76

[6] D.P. Sumner Critical concept in domination, Discrete Mathematics, Volume 86 (1990), pp. 33-46

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