Abstract
It is known that, given a graph G, finding a pair of vertices (v i ,v j ) such that v i 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 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 \(\leq_T^p\) GA.
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© 2007 Springer-Verlag Berlin Heidelberg
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Nagoya, T., Toda, S. (2007). Relating Complete and Partial Solution for Problems Similar to Graph Automorphism. In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_52
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DOI: https://doi.org/10.1007/978-3-540-74456-6_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74455-9
Online ISBN: 978-3-540-74456-6
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