Relating Complete And Partial Solution For Problems Similar To Graph Automorphism

It is known that, given a graph G, finding a pair of vertices (v(i), v(j)) such that of is mapped to v(j) by some non-trivial automorphism on G is as hard as computing a non-trivial automorphism. In this paper, we show that, given a graph G, computing even a single vertex that is snapped to a different vertex by a non-trivial automorphism is as hard as computing a non-trivial automorphism. We also show that Right GA has the same property. On the other hand, we show that if PrefixGA has this property then GI <= (p)(T) GA.