Geodesic
Efficient (j,k)-domination
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 409-423

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A dominating set S of a graph G is called efficient if |N[v]∩ S| = 1 for every vertex v ∈ V(G). That is, a dominating set S is efficient if and only if every vertex is dominated exactly once. In this paper, we investigate efficient multiple domination. There are several types of multiple domination defined in the literature: k-tuple domination, k-domination, and k-domination. We investigate efficient versions of the first two as well as a new type of multiple domination.
Keywords: efficient domination, multiple domination 
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Rubalcaba, Robert; Slater, Peter. Efficient (j,k)-domination. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 409-423. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a2/