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In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set. In other words, there is no vertex outside the independent set that may join it because it is maximal with respect to the independent set property. For example, in the graph P₃, a path with three vertices a, b, and c, and two edges ab and bc, the sets {b} and {a,c} are both maximally independent.