#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 jaanos):
Perhaps I was not being precise enough: I was talking about the generating
set of the Cayley graph, not about the generators of the group.
So, a user may want any of the following (where computing each relies on
the previous):
1. whether there exists a transitive subgroup of the automorphism group
with the same order as the graph,
2. one such group,
3. a map from vertices to group elements,
4. a (multi)set of group elements that acts as the generating set for the
Cayley graph.
Now, going from step 2 to steps 3 and 4 surely is not hard (4 lines of
code), but it is not something that can be done with a simple method call,
and step 4 it is certainly not something that can be computed from the
group itself.
Anyway, I was probably wrong that the map would be a better certificate
than the group, as the former is clearly easily computable from the
latter.
By the way, what we're actually looking for here is a regular subgroup, so
that's what the group method should be called (and we can also simplify
the GAP call).
Janoš
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Ticket URL: <http://trac.sagemath.org/ticket/19586#comment:39>
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