# CayleyGraph

CayleyGraph[group]

returns a Cayley graph representation of group.

# Details and Options

• CayleyGraph[group] returns a graph object with head Graph.
• A Cayley graph is both a description of a group and of the generators used to describe that group. The generators are those returned by the function GroupGenerators.
• Group elements are represented as vertices, and generators are represented as directed edges. An edge from a group element g1 to an element g2 means that the product of g1 with the generator of the edge gives g2.
• Vertices are numbered as ordered by GroupElements and GroupElementPosition. The identity element is always numbered 1.
• Generators are represented by default using different colors, following the sequence of colors used by Plot with several curves.

# Examples

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## Basic Examples(1)

This is the Cayley graph connecting the 24 elements of a permutation group defined by two generators, the first represented in blue and the second in green:

## Scope(3)

Cayley graph of the symmetric group of degree four defined by three transpositions:

Cayley graph of the symmetric group of degree four with the default generating set:

The identity permutation is removed from the list of generators:

## Possible Issues(1)

This is only a useful representation for small groups. For groups with a few hundred elements, the graph is generally already too complex:

## Neat Examples(1)

A point:

A line:

A square:

A cube:

A 4D cube:

A 5D cube:

Wolfram Research (2010), CayleyGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/CayleyGraph.html.

#### Text

Wolfram Research (2010), CayleyGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/CayleyGraph.html.

#### CMS

Wolfram Language. 2010. "CayleyGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CayleyGraph.html.

#### APA

Wolfram Language. (2010). CayleyGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CayleyGraph.html

#### BibTeX

@misc{reference.wolfram_2023_cayleygraph, author="Wolfram Research", title="{CayleyGraph}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/CayleyGraph.html}", note=[Accessed: 06-December-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_cayleygraph, organization={Wolfram Research}, title={CayleyGraph}, year={2010}, url={https://reference.wolfram.com/language/ref/CayleyGraph.html}, note=[Accessed: 06-December-2023 ]}