#16370: OA(k,n) strongly regular graphs
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.3
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | e469bb5b23d7862b48082f1cba9fd946dd7dc406
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/16370 |
Dependencies: |
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Comment (by vdelecroix):
Hi,
An OA does not determine uniquely a graph. As Kanappan said there are at
least three natural ones and there are many more non-trivial
constructions. So calling it `graphs.OrthogonalArrayGraph` completely
misleading.
About the syntax, let me cite Andries Brouwer:
If you have a set with a collection of subsets, that is called a
hypergraph, and the subsets are called hyperedges. Given a hypergraph, one
can make the intersection graph. The vertices of the hypergraph are the
hyperedges. Two distinct vertices are adjacent when their intersection is
nonempty. This is a construction that occurs in many different places. A
design is a hypergraph with certain regularity properties. But this
intersection graph is needed for many types of design.
It makes no sense to design a system where intersection graph gets
different names depending on the type of design one used as input.
So the name could be either `graphs.IntersectionGraphOfOneOrthogonalArray`
or simply a subcase of `graphs.IntersectionGraph`. And I am in favour of
the second one.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16370#comment:31>
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