Efficient Domination and Efficient Edge Domination: A Brief Survey

@inproceedings{Brandstdt2018EfficientDA,
  title={Efficient Domination and Efficient Edge Domination: A Brief Survey},
  author={Andreas Brandst{\"a}dt},
  booktitle={CALDAM},
  year={2018}
}
In a finite undirected graph \(G=(V,E)\), a vertex \(v \in V\) dominates itself and its neighbors in G. A vertex set \(D \subseteq V\) is an efficient dominating set (e.d.s. for short) of G if every \(v \in V\) is dominated in G by exactly one vertex of D. 
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References

SHOWING 1-10 OF 73 REFERENCES
New Polynomial Cases of the Weighted Efficient Domination Problem
TLDR
The Efficient Domination (ED) problem, which asks for the existence of an e.d. in G, is known to be \(\mathbb{NP}\)-complete even for very restricted graph classes.
Perfect edge domination and efficient edge domination in graphs
The Weighted Perfect Domination Problem and Its Variants
Weighted Efficient Domination for P5-Free Graphs in Linear Time
TLDR
It is shown that, based on modular decomposition, ED is solvable in linear time for $P_5$-free graphs.
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