Word.ws English Dictionary

Frucht's theorem

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.

Proper noun

Frucht's theorem

  1. 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.

Origin of Frucht's theorem

Proved by Robert Frucht in 1939.

Questions about Frucht's theorem

What does Frucht's theorem mean?
Frucht's theorem means 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.
What part of speech is Frucht's theorem?
Frucht's theorem is a proper noun.

Words near Frucht's theorem in the dictionary

  1. FRTs
  2. FRU
  3. fru-fru
  4. fru-frus
  5. Frubel
  6. Frucht's theorem
  7. Fruchter
  8. Fruchthandler
  9. fruchtschiefer
  10. fruck
  11. fruckies

Source and license

Adapted from Wiktionary: Frucht's theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “Frucht's theorem.” Word.ws, https://word.ws/frucht%27s_theorem. Based on Wiktionary, CC BY-SA 4.0.