#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: | 95dfa64264bb0e6ec9122e5ce458a5000d48bc3d
u/jaanos/add_is_cayley_graph | Stopgaps:
Dependencies: |
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Comment (by jaanos):
Hi!
Hmm, I would still like to have an `is_cayley` method for graphs. 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).
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?
Janoš
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Ticket URL: <http://trac.sagemath.org/ticket/19586#comment:29>
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