In graph theory, an edge dominating set for a graph G = (V, E) is a subset D ⊆ E such that every edge not in D is adjacent to at least one edge in D. An edge dominating set is also known as a line dominating set. Figures (a)–(d) are examples of edge dominating sets (thick red lines).
A minimum edge dominating set is a smallest edge dominating set. Figures (a) and (b) are examples of minimum edge dominating sets (it can be checked that there is no edge dominating set of size 2 for this graph).
Read more about Edge Dominating Set: Properties, Algorithms and Computational Complexity
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—Ralph Waldo Emerson (1803–1882)