GraphAutomorphismGroup

GraphAutomorphismGroup[g]

gives the automorphism group of a graph g.

GraphAutomorphismGroup[{vw,…}]

uses rules vw to specify the graph g.

Details

  • GraphAutomorphismGroup is typically used to enumerate isomorphic variants and symmetric structures 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.
  • GraphAutomorphismGroup[g] gives a PermutationGroup that represents the group of automorphisms of the graph g.

Examples

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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:

Wolfram Research (2014), GraphAutomorphismGroup, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphAutomorphismGroup.html (updated 2015).

Text

Wolfram Research (2014), GraphAutomorphismGroup, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphAutomorphismGroup.html (updated 2015).

CMS

Wolfram Language. 2014. "GraphAutomorphismGroup." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphAutomorphismGroup.html.

APA

Wolfram Language. (2014). GraphAutomorphismGroup. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphAutomorphismGroup.html

BibTeX

@misc{reference.wolfram_2025_graphautomorphismgroup, author="Wolfram Research", title="{GraphAutomorphismGroup}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphAutomorphismGroup.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_graphautomorphismgroup, organization={Wolfram Research}, title={GraphAutomorphismGroup}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphAutomorphismGroup.html}, note=[Accessed: 21-February-2025 ]}