Relating complete and partial solution for problems similar to graph automorphism

Authors:
Takayuki Nagoya;Seinosuke Toda
Affiliations:
Department of Mathematical Sciences, Tokyo Denki University;Department of Computer Science and System Analysis, College of Humanities and sciences, Nihon University
Venue:
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Year:
2007

Citing 4
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Abstract

It is known that, given a graph G, finding a pair of vertices (vi, 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.