  It is well-known [KST93] that the complexity of the Graph Automorphism
problem is characterized by a special case of Graph Isomorphism, where the
input graphs satisfy the "promise" of being rigid (that is, having no
nontrivial automorphisms). In this brief note, we observe that the reduction of
Graph Automorphism to the Rigid Graph Ismorphism problem can be accomplished
even using Grollman and Selman's notion of a "smart reduction".
