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.

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 $\mathrm{pq}=\mathrm{qp}$ 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.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

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

$G≔{\mathbf{S}}_4$

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

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

$G≔{\mathbf{D}}_7$

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

$G≔\mathrm{FrobeniusGroup}\left(72\,1\right)$

$G≔⟨\left(2\,3\,8\,9\,4\,6\,7\,5\right)\,\left(2\,8\,4\,7\right)\left(3\,9\,6\,5\right)\,\left(2\,4\right)\left(3\,6\right)\left(5\,9\right)\left(7\,8\right)\,\left(1\,2\,4\right)\left(3\,5\,7\right)\left(6\,8\,9\right)\,\left(1\,3\,6\right)\left(2\,5\,8\right)\left(4\,7\,9\right)⟩$

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

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

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