Frucht's theorem is a result in algebraic graph theory, conjectured by Dénes Kőnig in 1936[1] and proved by Robert Frucht in 1939.[2] It states 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.