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The k-Rainbow Domination and Domatic Numbers of Digraphs
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  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 1,  2016, pp.69-81
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.1.69
 Title & Authors
The k-Rainbow Domination and Domatic Numbers of Digraphs
Sheikholeslami, S.M.; Volkmann, Lutz;
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 Abstract
For a positive integer k, a k-rainbow dominating function of a digraph D is a function f from the vertex set V (D) to the set of all subsets of the set such that for any vertex with the condition is fulfilled, where is the set of in-neighbors of v. A set of k-rainbow dominating functions on D with the property that for each , is called a k-rainbow dominating family (of functions) on D. The maximum number of functions in a k-rainbow dominating family on D is the k-rainbow domatic number of D, denoted by . In this paper we initiate the study of the k-rainbow domatic number in digraphs, and we present some bounds for .
 Keywords
Digraph;k-rainbow dominating function;k-rainbow domination number;k-rainbow domatic number;
 Language
English
 Cited by
1.
Rainbow reinforcement numbers in digraphs, Asian-European Journal of Mathematics, 2016, 1750004  crossref(new windwow)
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