---
tag: W76DE2EQCY
kind: statement
role: theorem
name: Sabidussi's Theorem
msc: [05C25, 20F65]
sources:
  - wikipedia: en:358277@r1363694726
    locator: Cayley graph, section Characterization
    note: adopted
    mention: wikipedia://en/358277#8CNR
    sections: [Statement]
inventory: [834YRM5FRR]
---

## Statement

An (unlabeled and uncolored) directed graph $\Gamma$ is a Cayley graph of a group $G$ if and only if it admits a simply transitive action of $G$ by graph automorphisms (i.e., preserving the set of directed edges).