Efficient Dominating and Edge Dominating Sets for Graphs and Hypergraphs

@inproceedings{Brandstdt2016EfficientDA,
  title={Efficient Dominating and Edge Dominating Sets for Graphs and Hypergraphs},
  author={Andreas Brandst{\"a}dt and Ragnar Nevries},
  booktitle={Encyclopedia of Algorithms},
  year={2016}
}
Let G = (V,E) be a graph. A vertex dominates itself and all its neighbors, i.e., every vertex v ∈ V dominates its closed neighborhood N[v]. A vertex set D in G is an efficient dominating (e.d.) set for G if for every vertex v ∈ V, there is exactly one d ∈ D dominating v. An edge set M ⊆ E is an efficient edge dominating (e.e.d.) set for G if it is an efficient dominating set in the line graph L(G) of G. The ED problem (EED problem, respectively) asks for the existence of an e.d. set (e.e.d. set… 
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