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The k-Rainbow Bondage Number of a Digraph

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Amjadi J., Mohammadi N., Sheikholeslami S. M., Volkmann L.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 2

261-270

Let D = (V,A) be a finite and simple digraph. A k-rainbow dominating function (kRDF) of a digraph D is a function f from the vertex set V to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V with f(v) = Ø the condition ∪u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled, where N−(v) is the set of in-neighbors of v. The weight of a kRDF f is the value w(f) = ∑v∈V |f(v)|. The k-rainbow domination number of a digraph D, denoted by γrk(D), is the minimum weight of a kRDF of D. The k-rainbow bondage number brk(D) of a digraph D with maximum in-degree at least two, is the minimum cardinality of all sets A′ ⊆ A for which γrk(D−A′) > γrk(D). In this paper, we establish some bounds for the k-rainbow bondage number and determine the k-rainbow bondage number of several classes of digraphs.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Amjadi J.

1 Mohammadi N.

1 Sheikholeslami S. M.

1 Volkmann L.

1 2015

Wyniki wyszukiwania

The k-Rainbow Bondage Number of a Digraph