A minimal dominating set is a dominating set in a graph that is not a proper subset of any other dominating set. Every minimum dominating set is a minimal dominating set, but the converse does not necessarily hold. Minimal dominating sets can be used to compute the domatic number of a graph. A dominating set is minimal dominating iff it is irredundant. If a set is dominating and irredundant, it is maximal irredundant and minimal dominating.
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