[GAP Forum] Partitions and orbits of automorphism groups

[Sven Reichard]

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Am 11.07.2013 09:22, schrieb Ebrahim Ghorbani:
> Dear Forum,
> 
> I have a partition of the vertex set of a vertex-transitive graph
> G. I guess that this partition are the orbit partition of some
> subgroup of Aut(G). Is there any way to find out this?
> 
> Thanks, Ebrahim
> 
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Dear Ebrahim,

say the partition is P. If it is the orbit partition of some group of
automorphisms, then in particular it is the orbit partition of its own
stabilizer in the full group Aut(G). Thus, if P is given as a set of
sets, we can simply test as follows:

gap> stab := Stabilizer(Aut(G), P, OnSetsSets);
gap> Length(P) = Length(Orbits(stab, [1..G.order]));

(We just compare the lengths so we don't have to sort the orbits.)

Hope this helps,
Sven.

- --
Sven Reichard
Institut für Algebra
TU Dresden
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