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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] and let $k$ be a natural number.\nThe graph $G$ is $k$-regular, or regular of degree $k$, if each vertex of $G$ has [[degree|0T0F6CCS9W]] $k$.\nA graph is regular if it is $k$-regular for some $k$.\n\n## Remarks\n\nA $0$-regular graph has no edges. A $1$-regular graph is a perfect matching. A finite $2$-regular graph is a disjoint union of cycles.\nA $3$-regular graph is also called cubic. The [[Petersen graph|0NR95CTFCZ]] is cubic.\nThe complete graph $K_n$ is $(n-1)$-regular. By the [[handshaking lemma|0XAP8WHNES]], a finite $k$-regular graph on $n$ vertices has $kn/2$ edges.\n\n## Explanations\n\n### L1 human\n\nA graph is regular when all vertices have the same number of neighbours.\nThe corners and edges of a cube form a $3$-regular graph.\n",
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