Derya DOĞAN DURGUN, Ferhan Nihan ALTINDAĞ

2-Rainbow Domination Number of Some Graphs

ISSN: 1305-130X
Yayın Aralığı: 4
Başlangıç: 2005
Yayıncı: Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü

A 2-rainbow domination function of a graph G is a function f that assigns to each vertex a set ofcolors chosen from the set {1,2}, such that for any ? ∈ ?(?), ?(?) = ∅ implies ⋃?∈?(?) |?(?)| ={1,2}. The 2-rainbow domination number ??2(?) of a graph G is minimum w(?) = Σ?∈?(?) |?(?)|over all such functions f. In this paper, we show that upper bounds of 2-rainbow dominationnumbers of several classes of graphs.

Keywords:

Vulnerability, domination 2-rainbow domination, k  th power of a graph,

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Brešar B.; Henning M.A.; Rall D.F.; Paired-domination of Cartesian Products of Graphs and Rainbow Domination, Electronic Notes in Discrete Mathematics, 2005; 22, 233-237.
Brešar B.; Henning M.A.; Rall D.F.; Rainbow Domination in Graphs, Taiwanese Journal of Mathematics, 2008; 12 (1), 213-225.
Bre?̌?? B.; ? ̌ umenjak T.K.; On the 2-rainbow Domination in Graphs, Discrete Applied Mathematics, 2007; 155, 2394- 2400.
Chartrand G.; Lesniak L.; Zhang P; Graphs and Digraphs, Chapman and Hall/CRC Press. 5 edition, 2010.
Tong C; Lin X; Yang Y; Luo M.; 2-Rainbow Domination of Generalized Petersen Graphs P(n,2), Discrete Applied Mathematics. 2009; 157, 1932-1937.
Xu G.; 2-Rainbow Domination in Generalized Petersen Graphs P(n,3), Discrete Applied Mathematics, 2009; 157, 2570-2573.
Shao Z.; Liang M., On Rainbow Domination Number of Graphs, Information Sciences, 2014; 254, 225-234.