#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: | 4aaf3014fee5bb08d861636908d6733047d4a869
u/jaanos/add_is_cayley_graph | Stopgaps:
Dependencies: |
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Comment (by dimpase):
Replying to [comment:29 jaanos]:
> Hmm, I would still like to have an `is_cayley` method for graphs.
sure, such a method can just check whether `cayley_graph_group()` is
`None`.
> But I agree about having a method `transitive_subgroup` for permutation
groups. Still, I'm a bit > worried about cases when we have a large graph
with a relatively small automorphism group (say, twice the order of the
graph) - then finding an appropriate subgroup will be fast, but actually
returning it (so a Sage subgroup can be built) may make a non-negligible
contribution to the running time (since reading GAP output can be slow).
as a switch to `libgap` will happen sooner or later, optimising for not
reading GAP output
does not seem to be that important.
> So I propose:
> - we have a `transitive_subgroup` method, which by default returns a
transitive subgroup of given order,
> - `transitive_subgroup` may be explicitly told not to return the group
(by setting, say, `return_group` to `False`),
> - we add a helper method (say, `_transitive_subgroup_gap`) which returns
a GAP object containing the subgroup (we could make the result cached, so
if one first asks whether a graph is Cayley and then wants to know the
group, it needn't be recomputed).
>
> This way, `transitive_subgroup` can call the helper function, and then
avoid actually reading the GAP subgroup if it is told not to return it.
>
> What do you think?
this ceritainly looks better, but again, I don't like the counter-
intuitive parameters of `is_cayley()` and weird sort of output (a pair)
that you currently have. In particular the latter.
--
Ticket URL: <http://trac.sagemath.org/ticket/19586#comment:32>
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