Relating complete and partial solution for problems similar to graph automorphism

Abstract

It is known that, given a graph G, finding a pair of vertices (V i, vj) such that Vi is mapped to Vj 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 mapped to a different vertex by a non-trivial automorphism is as hard as computing a non-trivial automorphism. We also show that RightGA has the same property. On the other hand, we show that if PrefixGA has this property then GI ≤TP GA. © Springer-Vorlag Berlin Heidelberg 2007.