Editing Complement graph (section)

==Applications and examples==
Several graph-theoretic concepts are related to each other via complementation:
*The complement of an [[edgeless graph]] is a [[complete graph]] and vice versa.
*Any [[induced subgraph]] of the complement graph of a graph {{mvar|G}} is the complement of the corresponding induced subgraph in {{mvar|G}}.
*An [[independent set (graph theory)|independent set]] in a graph is a [[clique (graph theory)|clique]] in the complement graph and vice versa. This is a special case of the previous two properties, as an independent set is an edgeless induced subgraph and a clique is a complete induced subgraph.
*The [[Graph automorphism|automorphism]] group of a graph is the automorphism group of its complement.
*The complement of every [[triangle-free graph]] is a [[claw-free graph]],<ref>{{Citation
 | last1 = Chudnovsky | first1 = Maria | author1-link = Maria Chudnovsky
 | last2 = Seymour | first2 = Paul | author2-link = Paul Seymour (mathematician)
 | contribution = The structure of claw-free graphs
 | mr = 2187738
 | location = Cambridge
 | pages = 153–171
 | publisher = Cambridge Univ. Press
 | series = London Math. Soc. Lecture Note Ser.
 | title = Surveys in combinatorics 2005
 | contribution-url = http://www.math.princeton.edu/~mchudnov/claws_survey.pdf
 | volume = 327
 | year = 2005}}.</ref> although the reverse is not true.