By definition, the orbit of a vertex v in a graph G is the set of all vertices f(v) such that f is an automorphism of G.
I wonder whether there is a definition for a minimal set S of automorphisms of G which generates the orbit. That is, for a vertex v in the orbit, the set of all vertices h(v) such that h is an automorphism in S.
(The number of all elements of the minimal set is the same as the number of all elements of the orbit.)
If such a definition exists, what is it?