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  and a subset  of its elements, the commuting graph of  and  is the graph whose vertices are elements of  and for which two vertices  and  are adjacent if  in .

• 

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

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

(1)

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

(2)

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

(3)

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]

 


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