Hello!
I apologize for posting this question here but somehow I am not allowed to
drop questions to sage-support. Moreover I do not feel confident enough to
post this thing as a bug on the trac wiki.
Working with a large graph G on ~250 vertices I have noticed that elements
of the automorphism group of G permute ~50 vertices and that most vertices
are fixed by any automorphism. Hence most orbits of the automorphism group
contain just singletons. However sage simply discards all vertices that are
fixed by the automorphism . In my case this resulted in an "incomplete"
orbit containing just 50 elements. An extreme case happens when one deals
with an asymmetric graph
===
sage: G = graphs.RandomRegular(7,50)
sage: G.vertices()
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 47, 48, 49]
sage: G.automorphism_group().domain()
{1}
sage: G.automorphism_group().orbits()
[[1]]
===
This of course is not the desired result since one assumes orbits partition
the group.
Is this a bug or am I simply missing some parameter to resolve this issue?
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