Complement graph: Difference between revisions

Revision as of 10:31, 25 November 2021

Revision as of 19:35, 21 June 2022

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{{short description|Graph with same nodes but opposite connections as another}}

[[File:Petersen graph complement.svg|thumb|upright=1.35|The [[Petersen graph]] (on the left) and its complement graph (on the right).]]

In the [[mathematical]] field of [[graph theory]], the '''complement''' or '''inverse''' of a [[Graph (discrete mathematics)|graph]] {{mvar|G}} is a graph {{mvar|H}} on the same [[Vertex (graph theory)|vertices]] such that two distinct vertices of {{mvar|H}} are adjacent [[if and only if]] they are not adjacent in {{mvar|G}}. That is, to generate the complement of a graph, one fills in all the missing [[Edge (graph theory)|edges]] required to form a [[complete graph]], and removes all the edges that were previously there.<ref name="bm">{{citation

| last1=Bondy

| first1=John Adrian