#19586: Add is_cayley_graph
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Reporter: jaanos | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-7.1
Component: graph theory | Resolution:
Keywords: Cayley graphs | Merged in:
groups | Reviewers: Nathann Cohen
Authors: Janoš Vidali | Work issues:
Report Upstream: N/A | Commit:
Branch: | a58a7348bc022f39bf68383b70400e8b7f5b268b
u/jaanos/add_is_cayley_graph | Stopgaps:
Dependencies: |
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Comment (by jaanos):
Replying to [comment:83 dimpase]:
> it is certainly true that you can assume w=1. So you have the neighbours
of 1 in the graph (with its vertices labelled by the elements of G) say
g,,1,,,...,g,,k,,. Now you need an argument that g,,1,,,...,g,,k,,
generate G. I don't see it in what you wrote above.
If the graph is connected, they clearly do (if the graph is directed,
vertex-transitivity then implies that it is also strongly connected). But
they don't need to generate the group in the general case - it suffices
that we get an isomorphic graph from the Cayley construction.
Janoš
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Ticket URL: <http://trac.sagemath.org/ticket/19586#comment:84>
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