File:Transpositioncayleyons3.png

The Cayley graph on symmetric group:S3 with generating set the set of all transpositions. Note that since the generating set is a full conjugacy class of involutions, the left and right Cayley graphs are identical. Also, every edge here is given a direction of moving away from the identity element. This can be done because there are no cycles of odd length, which is because all the generators are odd permutations.