While another thread has folks thinking about graph automorphisms,
here is another one. Historically, graph vertices were integers
beginning at zero. Permutation groups in GAP have symbols beginning
with one.
The scheme employed is to "promote" vertex zero to the final symbol of
the permutation group. This will sometimes require a lot of manual
adjustements vioa the translation dictionary
Now graphs allow vertices that are other objects (like sets) and now,
thanks to Mike Hansen, permutation groups can work on arbitrary symbol
sets.
sage: G = SymmetricGroup(['a', 'b', 'c'])
sage: G.list()
[(), ('b','c'), ('a','b'), ('a','b','c'), ('a','c','b'), ('a','c')]
Current state of affairs leads to confusing situations like:
sage: G = Graph([(1,2),(2,3)], multiedge=False)
sage: A, T = G.automorphism_group(translation=True)
sage: T
{1: 3, 2: 1, 3: 2}
sage: A.list()
[(), (2,3)]
Does anyone have a workaround that will get integer vertices to align
with permutation group symbols? Has anyone made progress on getting
the graph isomorphism code to return the "real" vertices as the
symbols of the automorphism group?
Thanks,
Rob
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