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  "body": "\n## Statement\n\n**Frucht's theorem** is a result in algebraic graph theory, conjectured by Dénes Kőnig in 1936 and proved by Robert Frucht in 1939. It states that every finite group is the [[group of symmetries|0CWXCWP0Y0]] of a finite undirected graph. More strongly, for any finite group $G$, there exist infinitely many [[non-isomorphic|00CT0PTH74]] simple connected graphs such that the [[automorphism group|0CWXCWP0Y0]] of each of them is isomorphic to $G$.\n",
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