Math 2.0

Proposition

Frucht's theorem

Statement

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

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first. The path takes the proof Proof of Frucht's theorem.

Show the path as a graph
Proof of Frucht's theorem, proof, no evidence levelProof of Frucht's the…proofFrucht's theorem, statement, no evidence levelFrucht's theoremstatement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proof of Frucht's theorem proof
  2. Frucht's theorem statement

Further reading

  1. Wikipedia, page 26259599, revision 1327421226, Frucht's theorem. adopted
About this page
TagW7Q3ZPF46B
URIm2://W7Q3ZPF46B
Kindstatement, proposition
WritingW0 stub
StatusThis copy of the site has no build data. Run m2 status W7Q3ZPF46B.
Same as
Changed4 November 2026

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  • edge uses out: each definition that the statement needs (0 of 1)

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Proofs