Question: How to Graph a Permutation

Maple 2015

Using with(combinat) the permutation of {a,b,c} is determined.

>restart:
>with(combinat):
>permute({a, b, c})
                  [[a, b, c], [a, c, b], [b, a, c], [b, c, a], [c, a, b], [c, b, a]]

The tree diagram of this permutation is

In Maple, using with(combinat) and with(GraphTheory), when I attempt to draw the permutation I get the following error:

>L := permute({a, b, c});
       L := [[a, b, c], [a, c, b], [b, a, c], [b, c, a], [c, a, b], [c, b, a]]
>DrawGraph(L);
  Error, invalid input: GraphTheory:-DrawGraph expects its 1st argument, H, to be of type       {GRAPHLN, list(GRAPHLN), set(GRAPHLN)}, but received [[a, b, c], [a, c, b], [b, a, c], [b, c,      a], [c,   a, b], [c, b, a]]

On Maple, again using with(combinat) and with(GraphTheory) the command permute(3) is used.  The results are manually configured as node-connection lines.  A fair representation of the tree diagram is configured by Maple, although the diagram has numeric instead of alpha configurations, and the a,b,c structure shown above is not easily recognized.

Any suggestions on developing a procedure that will graph (draw) an alpha-labeled permutation welcomed.  Thanks!  WC44_Permutation_Graph.mw