Regular graph

Definition

Let $G$ be a graph and let $k$ be a natural number. The graph $G$ is $k$ -regular, or regular of degree $k$ , if each vertex of $G$ has degree $k$ . A graph is regular if it is $k$ -regular for some $k$ .

Remarks

A $0$ -regular graph has no edges. A $1$ -regular graph is a perfect matching. A finite $2$ -regular graph is a disjoint union of cycles. A $3$ -regular graph is also called cubic. The Petersen graph is cubic. The complete graph $K_n$ is $(n-1)$ -regular. By the handshaking lemma, a finite $k$ -regular graph on $n$ vertices has $kn/2$ edges.

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Graph definition
Neighbourhood definition
Degree of a vertex definition
Regular graph definition

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Tag	`0KA4S8R39M`
URI	`m2://0KA4S8R39M`
Kind	definition
Writing	W1 stated
MSC	05C07
Defines	Regular graph
Uses	Degree of a vertex

Regular graph

Definition

Remarks

Reading path

Where this leads

Further reading

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