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The k-rainbow domatic number of a graph

Seyyed Mahmoud Sheikholeslami; Lutz Volkmann — 2012

Discussiones Mathematicae Graph Theory

For a positive integer k, a k-rainbow dominating function 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 for any vertex v ∈ V(G) with f(v) = ∅ the condition ⋃u ∈ N(v)f(u) = 1,2, ...,k is fulfilled, where N(v) is the neighborhood of v. The 1-rainbow domination is the same as the ordinary domination. A set $f ₁, f ₂, . . ., f_{d}$ of k-rainbow dominating functions on G with the property that $\sum_{i = 1}^{d} | f_{i} (v) | \leq k$ for each v ∈ V(G), is called a k-rainbow dominating family (of...

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