#13874: Allow automorphism group of a graph to act on the graph's vertex set
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Reporter: azi | Owner: jason, ncohen, rlm
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.6
Component: graph theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Description changed by benjaminfjones:
Old description:
> The current implementation of the automorphism group of a graph always
> relabels the graph in question to use the vertex set $1,2,...,$ and then
> returns the automorphism group based on this labelling and potentially a
> translation for the labelling as well.
>
> Needless to say that this is time consuming, confusing and also prone to
> bugs since if one uses integers as labels (starting at 0 for example) the
> relabelling might go unnoticed.
>
> As it appears from [https://groups.google.com/forum/?fromgroups=#!topic
> /sage-devel/wLtbNpeYrok this] sage-devel post it is now possible to use
> arbitrary domains for permutation groups.
>
> Hence, it would be nice to integrate this change into the
> automorphism_group function as well.
New description:
The current implementation of the automorphism group of a graph always
relabels the graph in question to use the vertex set {1,2,...,n+1} and
then returns the automorphism group based on this labeling and potentially
a translation for the labeling as well.
Needless to say that this is time consuming, confusing and also prone to
bugs since if one uses integers as labels (starting at 0 for example) the
relabeling might go unnoticed.
As it appears from [https://groups.google.com/forum/?fromgroups=#!topic
/sage-devel/wLtbNpeYrok this] sage-devel post it is now possible to use
arbitrary domains for permutation groups.
Hence, it would be nice to integrate this change into the
automorphism_group function as well.
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From https://groups.google.com/d/msg/sage-devel/y_TuGhjLYJQ/8YBUmQaNsXUJ
> In the long term, I think the right solution is to copy what is done for
Galois groups of number fields: depending on a keyword option to
automorphism_group(), we should return either the abstract permutation
group (as is done now) or a group equipped with an action on the edges and
vertices of the graph.
> David
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13874#comment:2>
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