Restrained domination in trees

Domke, Gayla S.; Hattingh, Johannes H.; Henning, Michael A.; Markus, Lisa R.

doi:10.1016/s0012-365x(99)00036-9

Cited by 40 publications

(17 citation statements)

References 4 publications

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“…The restrained domination number γ r (G) is the minimum cardinality of a restrained dominating set of G. The restrained domination number was introduced by Domke et al [14] and has been studied by several author (see for example [12,13]). The restrained bondage number b r (G) of a nonempty graph G is the minimum cardinality among all sets of edges F ⊆ E (G) for which γ r (G −F ) > γ r (G).…”

Section: Introductionmentioning

confidence: 99%

The restrained rainbow bondage number of a graph

Amjadi¹,

Khoeilar²,

Dehgardi³

et al. 2018

Tamkang J. Math.

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Abstract.A restrained k-rainbow dominating function (RkRDF) of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2, . . . , k} such that forThe minimum weight of a restrained k-rainbow dominating function of G is called the restrained k-rainbow domination number of G, denoted by γ r r k (G). The restrained krainbow bondage number b r r k (G) of a graph G with maximum degree at least two is the minimum cardinality of all sets F ⊆ E (G) for which γ r r k (G − F ) > γ r r k (G). In this paper, we initiate the study of the restrained k-rainbow bondage number in graphs and we present some sharp bounds for b r r 2 (G). In addition, we determine the restrained 2-rainbow bondage number of some classes of graphs.

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Section: Introductionmentioning

confidence: 99%

The restrained rainbow bondage number of a graph

Amjadi¹,

Khoeilar²,

Dehgardi³

et al. 2018

Tamkang J. Math.

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“…The restrained domination number of G denoted by γ r (G) is the smallest cardinality of a restrained dominating set of G. Restrained domination in graphs has been studied in [6,7,[11][12][13] and elsewhere.…”

Section: Introductionmentioning

confidence: 99%

Secure Restrained Domination in Graphs

Pushpam

Suseendran²

2015

Math.Comput.Sci.

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“…In this paper, we continue the study of a variation of the domination theme, namely that of restrained domination [3][4][5]11,12]. A set S ⊆ V is a restrained dominating set (RDS) if every vertex not in S is adjacent to a vertex in S and to a vertex in V − S. Every graph has a RDS, since S = V is such a set.…”

Section: Introductionmentioning

confidence: 99%

Restrained bondage in graphs

Hattingh

Plummer

2008

Discrete Mathematics

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Let G = (V, E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γ r (G), is the smallest cardinality of a restrained dominating set of G. We define the restrained bondage number b r (G) of a nonempty graph G to be the minimum cardinality among all sets of edges E ⊆ E for which γ r (G − E ) > γ r (G). Sharp bounds are obtained for b r (G), and exact values are determined for several classes of graphs. Also, we show that the decision problem for b r (G) is NP-complete even for bipartite graphs.

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Restrained domination in trees

Cited by 40 publications

References 4 publications

The restrained rainbow bondage number of a graph

The restrained rainbow bondage number of a graph

Secure Restrained Domination in Graphs

Restrained bondage in graphs

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