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.

$G≔\mathrm{GroupTheory}:-\mathrm{SymmetricGroup}\left(4\right)$

$G≔{\mathbf{S}}_4$

$\mathrm{GraphTheory}:-\mathrm{DrawGraph}\left(\mathrm{GroupTheory}:-\mathrm{CayleyGraph}\left(G\right)\,\mathrm{style}=\mathrm{spring}\right)$

$G≔\mathrm{GroupTheory}:-\mathrm{DihedralGroup}\left(7\right)$

$G≔{\mathrm{D}}_7$

$\mathrm{GraphTheory}:-\mathrm{DrawGraph}\left(\mathrm{GroupTheory}:-\mathrm{CayleyGraph}\left(G\right)\,\mathrm{style}=\mathrm{spring}\right)$

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

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

For more information on Maple 2015 changes, see Updates in Maple 2015.