#19586: Add is_cayley_graph
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Reporter: jaanos | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: graph theory | Resolution:
Keywords: Cayley graphs | Merged in:
groups | Reviewers:
Authors: Janoš Vidali | Work issues:
Report Upstream: N/A | Commit:
Branch: | baba4a8d4919be000984d40f56db542557c55e51
u/jaanos/add_is_cayley_graph | Stopgaps:
Dependencies: |
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Comment (by jaanos):
I have finally gotten around to continuing work on this ticket. So, now
we've got this:
* I have added a method `cayley_graph_group`, as suggested, which takes
care of obtaining the group (or actually computing it in the case of
disconnected graphs). It can be instructed not to actually return the
group, but only to tell whether the graph is Cayley or not.
* `is_cayley` calls the above method, requesting the group if a
certificate is requested. The certificate is now a copy of the graph with
edges labelled by members of the generating set, and vertices associated
to group elements (vertex names are not changed). One may then test that
the result is indeed a Cayley graph - an example is in the doctest. Of
course, once we will have a separate class/backend for Cayley graphs, we
can use that here.
* Since `set_edge_label` does not work for multiedges, I have added three
new parameters to `copy`. One is `data`, specifying the actual graph data
to be copied (so this can be anything `Graph` and `DiGraph` accept - in
this case, a list of vertices and a list of labelled edges). The other two
are `loops` and `multiedges` (I don't actually use them in the final
version, but I figured it might be still useful to keep them). Any of the
properties of the graph not specified as a parameter are obtained from the
graph itself, not from whatever `data` is.
So, what do you guys think?
Janoš
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=baba4a8d4919be000984d40f56db542557c55e51
baba4a8]||{{{Add cayley_graph_group and change the certificate to a
labelled graph}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/19586#comment:52>
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