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  "body": "\n## Definition\n\nLet $G$ and $H$ be [[graphs|0JD5C82QMB]] with vertex sets $V(G)$ and $V(H)$.\nA graph isomorphism from $G$ to $H$ is a bijection $f : V(G) \\to V(H)$ such that, for all $u, v \\in V(G)$,\n$$u \\sim v \\text{ in } G \\iff f(u) \\sim f(v) \\text{ in } H.$$\nThe graphs $G$ and $H$ are isomorphic, written $G \\cong H$, if there is an isomorphism between them.\n\n## Remarks\n\nIsomorphic graphs have the same number of vertices and edges and the same degrees. They differ only in the names of their vertices.\nAn isomorphism from $G$ to itself is an automorphism of $G$.\nThe path $P_4$ is isomorphic to its own [[complement|0RNMP6VCR2]].\n\n## Explanations\n\n### L1 human\n\nTwo graphs are isomorphic when one is a relabelling of the other.\nTwo drawings can look very different and still show isomorphic graphs.\n",
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