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Published in:
2009 | OriginalPaper | Chapter
Representing Groups on Graphs
Authors : Sagarmoy Dutta, Piyush P. Kurur
Published in: Mathematical Foundations of Computer Science 2009
Publisher: Springer Berlin Heidelberg
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In this paper we formulate and study the problem of representing groups on graphs. We show that with respect to polynomial time Turing reducibility, both abelian and solvable group representability are all equivalent to graph isomorphism, even when the group is presented as a permutation group via generators. On the other hand, the representability problem for general groups on trees is equivalent to checking, given a group
G
and
n
, whether a nontrivial homomorphism from
G
to
S
n
exists. There does not seem to be a polynomial time algorithm for this problem, in spite of the fact that tree isomorphism has polynomial time algorithms.