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Frucht's theorem

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 G {\displaystyle G} , there exist infinitely many non-isomorphic simple connected graphs such that…

Standards, Special families of graphs & Infinite graphs and groups

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Special families of graphs

3-regular graphsFrucht graphTrivial groupGert SabidussiRegular graphs
24 related topics

Infinite graphs and groups

Uncountably manyJohannes de GrootAxiom of choiceAxiom of regularity
4 related topics

Graph size

OrbitsVertex-transitive graph
2 related topics

Proof idea

Cayley graph
1 related topics

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Graph size

Special families of graphs

Infinite graphs and groups

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Frucht's theorem

Nodes63
Edges62
Triples22
Avg. degree1.97
Density0.031746
Components1

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Frucht's theorem

Top relations

related to Special families of graphs · 13
Frucht's theorem → Birkhoff's, Camille Jordan, Every, From, Frucht, Frucht's, Gert Sabidussi, However, It, László Babai, More, Planar, There
related to Infinite graphs and groups · 8
Frucht's theorem → Finally, Frucht's, Furthermore, Gert Sabidussi, Groot, Izbicki, Johannes, ZF
is a · 1
Frucht's theorem → result in algebraic graph theory

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Important terminology

group graph finite graphs groups symmetries every doi mr many infinite issn symmetry vertices 10 theorem frucht simple edges order

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Frucht's theoremis aresult in algebraic graph theory0.90text
Frucht's theoremrelated to Infinite graphs and groupsIzbicki0.60section
Frucht's theoremrelated to Infinite graphs and groupsFinally0.60section
Frucht's theoremrelated to Infinite graphs and groupsJohannes0.60section
Frucht's theoremrelated to Infinite graphs and groupsGroot0.60section
Frucht's theoremrelated to Infinite graphs and groupsGert Sabidussi0.60section
Frucht's theoremrelated to Infinite graphs and groupsFurthermore0.60section
Frucht's theoremrelated to Infinite graphs and groupsZF0.60section
Frucht's theoremrelated to Infinite graphs and groupsFrucht's0.60section
Frucht's theoremrelated to Special families of graphsThere0.60section
Frucht's theoremrelated to Special families of graphsFrucht's0.60section
Frucht's theoremrelated to Special families of graphsFrucht0.60section

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