#16370: OA(k,n) strongly regular graphs
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Reporter: | Owner:
ncohen | Status: needs_work
Type: | Milestone: sage-6.3
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | 90a72bd39d74c24cb548e5b7dc5995c67ac386f8
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/16370 |
Dependencies: |
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Changes (by vdelecroix):
* status: needs_review => needs_work
Comment:
Hi Nathann,
Could you write in the docs:
- how the graph is built
- what are the parameters (v=n^2^, k=k(n-1), lambda=(k-1)(k-2)+n-2,
mu=k(k-1))
Might also be good in the doctests, i.e.
{{{
sage: OA = designs.WHATEVER_OA(3,7)
sage: G = graphs.OrthogonalArrayGraph(OA)
sage: G.vertices()
...
sage: G.is_strongly_regular(parameters=True)
(49, 18, 7, 6)
sage: 7^2, 3*(7-1), (3-1)*(3-2)+7-2, 3*(3-1)
(49, 18, 7, 6)
}}}
The graph depends on the OA(k,n), doesn't it? It might really be that we
already have for some parameters several constructions of OA... and hence
as many OA-graphs. Would it be possible to have more open input, like
{{{def OrthogonalArrayGraph(data, n=None)}}} returning what you did if
`data=k` and `n=n` but also returns what we think if `data` is set to an
`OA`?
The construction is actually much more general: from any set of subsets we
can build such a graph. Wikipedia calls it an
[[http://en.wikipedia.org/wiki/Intersection_graph|Intersection graph]]
(note: any graph can be obtained that way). When the set of subsets is a
transversal design the obtained graph has nice properties but I am quite
sure that implementing `graphs.IntersectionGraph` would make more sense.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16370#comment:10>
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