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GroupTheory

 CayleyGraph
 construct the Cayley graph of a group

 Calling Sequence CayleyGraph( G ) CayleyGraph( G, elements = E, generators = S )

Parameters

 G - a small group E - (optional) list ; an ordering of the elements of G S - (optional) list ; a list of generators for G

Description

 • The Cayley graph of a (small) group $G$ is a directed graph encoding the abstract structure of $G$.
 • The CayleyGraph( G ) command returns the Cayley graph of the group G, in which the elements of G have been labeled by the integers 1..n, where n is the order of G.
 • You can specify a particular ordering for the elements of the group by passing the optional argument elements = E, where E is an explicit list of the members of G.
 • Note that computing the Cayley graph of a group requires that all the group elements be computed explicitly, so the command should only be used for groups of modest size.

Examples

Draw the Cayley graph of the symmetric group of degree 4.

 > $G≔\mathrm{GroupTheory}:-\mathrm{SymmetricGroup}\left(4\right)$
 ${G}{≔}{{\mathbf{S}}}_{{4}}$ (1)
 > $\mathrm{GraphTheory}:-\mathrm{DrawGraph}\left(\mathrm{GroupTheory}:-\mathrm{CayleyGraph}\left(G\right),\mathrm{style}=\mathrm{spring}\right)$ Draw the Cayley graph of the dihedral group of degree 7.

 > $G≔\mathrm{GroupTheory}:-\mathrm{DihedralGroup}\left(7\right)$
 ${G}{≔}{{\mathrm{D}}}_{{7}}$ (2)
 > $\mathrm{GraphTheory}:-\mathrm{DrawGraph}\left(\mathrm{GroupTheory}:-\mathrm{CayleyGraph}\left(G\right),\mathrm{style}=\mathrm{spring}\right)$ References

 "Cayley graph", Wikipedia. http://en.wikipedia.org/wiki/Cayley_graph

Compatibility

 • The GroupTheory[CayleyGraph] command was introduced in Maple 2015.