Abstract
The k-rainbow domination problem is studied for regular graphs. We prove that the k-rainbow domination number γrk(G) of a d-regular graph for d≤k≤2d is bounded below by kn∕2d, where n is the order of a graph. We determine necessary conditions for regular graphs to attain this bound and find several examples. As an application, we determine exact k-rainbow domination numbers for all cubic Cayley graphs over abelian groups.
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