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*An [[independent set (graph theory)|independent set]] in a graph is a [[clique (graph theory)|clique]] in the complement graph and vice versa.
*The complement of any [[triangle-free graph]] is a [[claw-free graph]].
*A [[self-complementary graph]] is a graph that is [[graph isomorphism|isomorphic]] to its own complement.<ref name="bm"/> Examples include the four-vertex [[path graph]] and five-vertex [[cycle graph]].
*[[Cograph]]s are defined as the graphs that can be built up from [[disjoint union]] and complementation operations, and form a self-complementary family of graphs: the complement of any cograph is another (possibly different) cograph.
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