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.
@article{bwmeta1.element.doi-10_7151_dmgt_1797,
author = {Jafar Amjadi and Negar Mohammadi and Seyed Mahmoud Sheikholeslami and Lutz Volkmann},
title = {The k-Rainbow Bondage Number of a Digraph},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {261-270},
zbl = {1311.05142},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1797}
}
Jafar Amjadi; Negar Mohammadi; Seyed Mahmoud Sheikholeslami; Lutz Volkmann. The k-Rainbow Bondage Number of a Digraph. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 261-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1797/
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