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  "body": "\n## Definition\n\nLet $G$ be a finite [[graph|0JD5C82QMB]] with a nonempty vertex set $V$.\nThe minimum degree of $G$ is\n$$\\delta(G) = \\min_{v \\in V} \\deg(v),$$\nthe smallest [[degree|0T0F6CCS9W]] of a vertex of $G$.\n\n## Remarks\n\nThe [[maximum degree|0KNAN9F27P]] $\\Delta(G)$ is the largest degree. Always $\\delta(G) \\le \\Delta(G)$.\nEach [[cycle graph|0QQ0F12962]] has $\\delta = 2$, and each tree with at least two vertices has $\\delta = 1$.\nA condition on $\\delta(G)$ gives a Hamiltonian cycle in [[Dirac's theorem|0TC99BRSSB]].\n\n## Explanations\n\n### L1 human\n\nThe minimum degree is the smallest number of edges at any vertex.\nIf $\\delta(G) = 3$, then each vertex has at least three neighbours.\n",
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