Properties
Further information: Dominating set#Independent dominationAn edge dominating set for G is a dominating set for its line graph L(G) and vice versa.
Any maximal matching is always an edge dominating set. Figures (b) and (d) are examples of maximal matchings.
Furthermore, the size of a minimum edge dominating set equals the size of a minimum maximal matching. A minimum maximal matching is a minimum edge dominating set; Figure (b) is an example of a minimum maximal matching. A minimum edge dominating set is not necessarily a minimum maximal matching, as illustrated in Figure (a); however, given a minimum edge dominating set D, it is easy to find a minimum maximal matching with |D| edges (see, e.g., Yannakakis & Gavril 1980).
Read more about this topic: Edge Dominating Set
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