#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:44 ncohen]:
> Hmmmm.. True. Returning a graph whose vertices are group elements and
whose edges are labelled with a group element looks cool. Plus one can
even get the actual group from `anyvertex.parent()`...
vertices and edge labels ought to be words in group generators (you always
need at most log_2(n) generators, at least if my memory is correct that
the elementary abelian 2-groups are the worst case for the number of
generators; and multiplying permutations is fast).
Actually, all you need to store is
[https://en.wikipedia.org/wiki/Schreier_vector "Schreier vector"], and
compute vertex and edge labels on the fly.
Certainly keeping edge labels for each edge is silly, as they are
trivially computed from the edge labels for one fixed vertex.
--
Ticket URL: <http://trac.sagemath.org/ticket/19586#comment:45>
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