Frucht's theorem

proper noun

The statement that every finite group is the group of symmetries of a finite undirected graph. More strongly, for any finite group G there exist infinitely many non-isomorphic simple connected graphs such that the automorphism group of each of them is isomorphic to G.

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Meanings

proper noun
  1. graph theoryThe statement that every finite group is the group of symmetries of a finite undirected graph. More strongly, for any finite group G there exist infinitely many non-isomorphic simple connected graphs such that the automorphism group of each of them is isomorphic to G.

Origin

Proved by Robert Frucht in 1939.

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Cite this entry
APA

Frucht's theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Frucht's%20theorem

MLA

“Frucht's theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Frucht's%20theorem. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Frucht's theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Frucht's%20theorem.

Source: Frucht's theorem on Wiktionary, CC BY-SA 4.0.