#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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Comment (by ncohen):
Y666666666666 !!
> Could you write in the docs:
> - how the graph is built
Isn't that written already ?..
{{{
The intersection graph of the block of a `TD(k,n)` (see
+ :func:`~sage.combinat.designs.orthogonal_arrays.orthogonal_array`) is
a
+ strongly regular graph.
}}}
That's a definition of the graph.
> - what are the parameters (v=n^2^, k=k(n-1), lambda=(k-1)(k-2)+n-2,
mu=k(k-1))
The parameters associated with a strongly regular graph.
{{{
sage: Graph.is_strongly_regular??
}}}
> 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)
> }}}
I don't get what you want me to add.... Only a call to `G.vertices()` ?
Brouwer gives the actual parameters of the final OA graph but I don't do
this in the docstring, so well....
> The graph depends on the OA(k,n), doesn't it?
Yes.
> 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`?
We could have a graph constructos `graphs.IntersectionGraph` taking as an
argument a list of sets and returning the corresponding graph. Would make
more sense than a dedicated version for 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.
Ahem. I should read the email before I answer them. Indeed, indeed `:-P`
Nathann
--
Ticket URL: <http://trac.sagemath.org/ticket/16370#comment:11>
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