Complement graph

Builds on Graph

Definition

Let $G = (V, E)$ be a graph. The complement of $G$ is the graph $\overline{G}$ with vertex set $V$ . Two distinct vertices are adjacent in $\overline{G}$ if and only if they are not adjacent in $G$ .

Remarks

The complement of the complement of $G$ is $G$ . The complement of the complete graph $K_n$ is the graph on $n$ vertices with no edges. A clique of $G$ is an independent set of $\overline{G}$ . This links Ramsey numbers to colourings of $K_n$ .

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Graph definition
Complement graph definition

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Strong perfect graph theorem

Tag	`0RNMP6VCR2`
URI	`m2://0RNMP6VCR2`
Kind	definition
Writing	W1 stated
MSC	05C76
Defines	Complement graph
Uses	Graph

Complement graph

Definition

Remarks

Reading path

Where this leads

Further reading

What this page needs for W2

What links here

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