>>
>> The documentation (G.automorphism_group?) describes how to get the
>> subgroup of the automorphism group that preserves a given partition of
>> the vertex set.
>
> The documentation about the partition thing is quite shallow (just one
> sentence) and the expected usage does not seem to work:
> ===
> sage: G = graphs.PetersenGraph()
> sage: G.automorphism_group(partition=[[1]])
> ---------------------------------------------------------------------------
> KeyError Traceback (most recent call last)
>
> /home/foo/<ipython console> in <module>()
>
> /home/foo/sage-5.5.rc0/local/lib/python2.7/site-packages/sage/graphs/generic_graph.pyc
> in automorphism_group(self, partition, translation, verbosity, edge_labels,
> order, return_group, orbits)
> 16466 HB = H._backend
> 16467 for u,v in self.edge_iterator(labels=False):
>> 16468 u = G_to[u]; v = G_to[v]
> 16469 HB.add_edge(u,v,None,self._directed)
> 16470 GC = HB._cg
>
> KeyError: 0
>
> =====
>
> does anyone happen to know how is this thing used? I need to compute the
> automorphism group that fixes the specified vertex (the stabilizer of a
> vertex v of the automorphism of G)
The partition you give should be a partition of the vertex set.
`partition=[[1]]` would only work if you had a vertex set {1}. Here
are some examples:
sage: G = graphs.PetersonGraph()
sage: G.vertices()
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
sage: G.automorphism_group(partition=[[0], [1..9]])
Permutation Group with generators [(3,7)(4,5)(8,9),
(2,6)(3,8)(4,5)(7,9), (1,4,5)(2,3,8,6,9,7)]
sage: G.automorphism_group(partition=[[0,1,2], [3..9]])
Permutation Group with generators [(3,7)(4,5)(8,9), (2,10)(3,5)(4,7)]
--
Benjamin Jones
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