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GLOBAL RAINBOW DOMINATION IN GRAPHS

J. Amjadi, S. M. Sheikholeslami, L. Volkmann
Published 2017 · Mathematics

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For a positive integer k, a k-rainbow dominating function (kRDF) of a graph G is a function f from the vertex set V.G/ to the set of all subsets of the set f1;2; : : : ;kg such that for any vertex v 2 V.G/ with f .v/ D ¿, the condition S u2N.v/f .u/ D f1;2; : : : ;kg is fulfilled, where N.v/ is the neighborhood of v. The weight of a kRDF f is the value !.f / D P v2V jf .v/j. A kRDF f is called a global k-rainbow dominating function (GkRDF) if f is also a kRDF of the complement G of G. The global k-rainbow domination number of G, denoted by grk.G/, is the minimum weight of a GkRDF on G. In this paper, we initiate the study of the global k-rainbow domination number and we establish some sharp bounds for it. 2010 Mathematics Subject Classification: 05C69
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