---
tag: W7Q3ZPF46B
kind: statement
role: proposition
name: Frucht's theorem
sources:
  - wikipedia: en:26259599@r1327421226
    locator: Frucht's theorem
    note: adopted
    mention: wikipedia://en/26259599
    sections: [Statement]
same_as:
  wikidata: Q1424481
  wikipedia: Frucht's theorem
inventory: [NC53Z4JNMP]
---

## 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|0CWXCWP0Y0]] of a finite undirected graph. More strongly, for any finite group $G$, there exist infinitely many [[non-isomorphic|00CT0PTH74]] simple connected graphs such that the [[automorphism group|0CWXCWP0Y0]] of each of them is isomorphic to $G$.