construct the Cayley graph of a group
CayleyGraph( G )
CayleyGraph( G, elements = E, generators = S )
a small group
(optional) list ; an ordering of the elements of G
(optional) list ; a list of generators for G
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.
By default, the set of generators used by the CayleyGraph command is the set that is returned by Generators( G ). To specify a different set of generators, use the generators=S option, where S is a set of generators of the group 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.
Draw the Cayley graph of the symmetric group of degree 4.
G ≔ SymmetricGroup⁡4
Draw the Cayley graph of the dihedral group of degree 7.
G ≔ DihedralGroup⁡7
The default set of generators for the group PGL⁡2,3 is given by the following command.
G ≔ PGL⁡2,3:
These are used by default for the Cayley graph.
To specify a different generating set, use the generators= option.
The simple group of order 168 is 2,3-generated.
G ≔ PSL⁡3,2:
It is also generated by the involution above and and element of order 7, leading to a very different Cayley graph.
"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.
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