The<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math>-rainbow bondage number of a graph

Dehgardi, Nasrin; Sheikholeslami, Seyed Mahmoud; Volkmann, Lutz

doi:10.1016/j.dam.2014.05.006

Cited by 17 publications

(17 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Dehgardi et al [128] introduced the concept of -rainbow bondage number of graphs. Let be a graph with maximum degree at least two.…”

Section: Conjecture 165 (Akbari Et Al [125] 2012) the Roman Bondagmentioning

confidence: 99%

See 1 more Smart Citation

On Bondage Numbers of Graphs: A Survey with Some Comments

2013

International Journal of Combinatorics

View full text Add to dashboard Cite

The domination number of a graph is the smallest number of vertices which dominate all remaining vertices by edges of . The bondage number of a nonempty graph is the smallest number of edges whose removal from results in a graph with domination number greater than the domination number of . The concept of the bondage number was formally introduced by Fink et al. in 1990. Since then, this topic has received considerable research attention and made some progress, variations, and generalizations. This paper gives a survey on the bondage number, including known results, conjectures, problems, and some comments, also selectively summarizes other types of bondage numbers.

show abstract

“…Dehgardi et al [128] introduced the concept of -rainbow bondage number of graphs. Let be a graph with maximum degree at least two.…”

Section: Conjecture 165 (Akbari Et Al [125] 2012) the Roman Bondagmentioning

confidence: 99%

“…The 2-rainbow bondage number of some special families of graphs has been determined. Theorem 174 (Dehgardi et al [128]). For any tree of order ⩾ 3, 2 ( ) ⩽ 2.…”

Section: Conjecture 165 (Akbari Et Al [125] 2012) the Roman Bondagmentioning

confidence: 99%

On Bondage Numbers of Graphs: A Survey with Some Comments

2013

International Journal of Combinatorics

View full text Add to dashboard Cite

show abstract

“…The k-rainbow domination number of G, denoted by γ rk (G), is the minimum weight of a kRDF of G. A kRDF f of G is a γ rk -function if ω( f ) = γ rk (G). The k-rainbow domination number was introduced by Brešar, Henning, and Rall [1] was studied by several authors (see, for example [2][3][4][5][6][7][8][9][10][11][12][13][14][15]).…”

Section: Introductionmentioning

confidence: 99%

k-Rainbow Domination Number of P3□Pn

et al. 2019

View full text Add to dashboard Cite

Let k be a positive integer, and set [ k ] : = { 1 , 2 , … , k } . For a graph G, a k-rainbow dominating function (or kRDF) of G is a mapping f : V ( G ) → 2 [ k ] in such a way that, for any vertex v ∈ V ( G ) with the empty set under f, the condition ⋃ u ∈ N G ( v ) f ( u ) = [ k ] always holds, where N G ( v ) is the open neighborhood of v. The weight of kRDF f of G is the summation of values of all vertices under f. The k-rainbow domination number of G, denoted by γ r k ( G ) , is the minimum weight of a kRDF of G. In this paper, we obtain the k-rainbow domination number of grid P 3 □ P n for k ∈ { 2 , 3 , 4 } .

show abstract

“…The k-rainbow bondage number b r k (G) for usual k-rainbow domination number was introduced by Dehgardi et al in [11] and has been studied by several authors [4,6].…”

Section: Introductionmentioning

confidence: 99%

The restrained rainbow bondage number of a graph

Amjadi¹,

Khoeilar²,

Dehgardi³

et al. 2018

Tamkang J. Math.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Thek-rainbow bondage number of a graph

Cited by 17 publications

References 18 publications

On Bondage Numbers of Graphs: A Survey with Some Comments

On Bondage Numbers of Graphs: A Survey with Some Comments

k-Rainbow Domination Number of P3□Pn

The restrained rainbow bondage number of a graph

Contact Info

Product

Resources

About