gives the automorphism group of a graph g.


uses rules vw to specify the graph g.


  • GraphAutomorphismGroup[g] gives a PermutationGroup that represents the group of automorphisms of the graph g.
  • The automorphism group for a graph can be used to enumerate isomorphic variants of a graph.
  • An automorphism of the graph g is a permutation of vertices of g that preserves the edge-vertex connectivity, i.e. if is an edge in g then is also an edge in g.


open allclose all

Basic Examples  (1)

Find the automorphism group of the PetersenGraph:

The number of elements of the group:

Scope  (4)

GraphAutomorphismGroup works with undirected graphs:

Directed graphs:

Use rules to specify the graph:

GraphAutomorphismGroup works with large graphs:

Introduced in 2014
Updated in 2015