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Efficient \((j,k)\)-domination. (English) Zbl 1142.05062

Summary: A dominating set \(S\) of a graph \(G\) is called efficient if \(|N[v]\cap S|=1\) for every vertex \(v\in V(G\). 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.

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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