#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 azi:
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,...,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.
>
> ----
>
> 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
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.
----
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
---
Also what appears to be a 'defect' is that if you have a graph G on say
150 vertices and you want to compute the stabilizer (or some other
subgroup..) of Aut(G) and you do
{{{
A = G.automorphism_group()
S = A.stabilizer(v)
}}}
it happens that you lose the information about the vertices of G. Since S
can be a group on a smaller domain and there is no translation from it to
the vertices of G
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13874#comment:3>
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