GroupTheory/CommutingGraph - Maple Help
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GroupTheory

  

CommutingGraph

  

construct the commuting graph of a group

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

Calling Sequence

CommutingGraph( G )

CommutingGraph( G, elements = E )

Parameters

G

-

a small group

E

-

(optional) list, set, or one of the names all or noncentral

Options

• 

elements = list, set, or one of the names all or noncentral

  

Specifies a selection of the elements of G to include as vertices of the generated graph.

  

If elements is a list or set, these elements are included.

  

If elements is noncentral, all elements of G except central elements are included.

  

If elements is all (the default), all elements of G are included.

Description

• 

For a finite group G and a subset E of its elements, the commuting graph of G and E is the graph whose vertices are elements of E and for which two vertices p and q are adjacent if pq=qp in G.

• 

The CommutingGraph( G ) command returns the commuting graph 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 commuting 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

withGroupTheory:

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

GSymmetricGroup4

GS4

(1)

GraphTheory:-DrawGraphCommutingGraphG,style=spring

Draw the commuting graph of the dihedral group of degree 7.

GDihedralGroup7

GD7

(2)

GraphTheory:-DrawGraphCommutingGraphG,style=spring

Draw the commuting graph of a Frobenius group of order 72.

GFrobeniusGroup72,1

G < a permutation group on 9 letters with 5 generators >

(3)

GraphTheory:-DrawGraphCommutingGraphG&comma;style&equals;spring

Compatibility

• 

The GroupTheory[CommutingGraph] command was introduced in Maple 2023.

• 

For more information on Maple 2023 changes, see Updates in Maple 2023.

See Also

GraphTheory

GroupTheory

GroupTheory[CayleyGraph]