#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
Old description:
> Turns out that orthogonal arrays give strongly regular graphs. Isn't that
> cool ?
>
> Brouwer's website is filled with references to "OA" `:-)`
>
> http://www.win.tue.nl/~aeb/graphs/srg/srgtab251-300.html
> http://www.win.tue.nl/~aeb/graphs/OA.html
>
> Nathann
New description:
Turns out that orthogonal arrays give strongly regular graphs. Isn't that
cool ?
Brouwer's website is filled with references to "OA" `:-)`
- http://www.win.tue.nl/~aeb/graphs/srg/srgtab251-300.html
- http://www.win.tue.nl/~aeb/graphs/OA.html
Nathann
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Comment:
Replying to [comment:17 ncohen]:
> [...]
>
> Tell me if my answers above convinced you.
Yes: this ticket should not go without a `graphs.IntersectionGraph`. And
intersection graphs of non-trivial BIBD are regular graph. So it is worth
to have them at least in the doc of `graphs.IntersectionGraph`.
For the parameters: they are explicit in terms of (k,n) for TD and (v,k)
for BIBD.
* for TD(k,n): lambda=(k-1)(k-2)+n-2, mu=k(k-1)
* for BIBD(v,k): lambda=(k-1)^2^+(v-1)/(k-1)-2, mu=k^2^
and this should be mentioned and tested.
By the way, why is there no BIBD in the Brouwer table?
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/16370#comment:19>
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