#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 ncohen):
Okay, as you quoted his email but did not quote what I answered to him I
paste it here.
----------
> 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.
It does.
All graphs are intersection graphs, and yet we have different functions to
create graphs.
Petersen's graph is a Kneser Graph, yet we have both a
`graphs.PetersenGraph` and a `graphs.KneserGraph` function.
There are different ways to create several graphs, and sometimes the
planar embeddings associated with them changes depending on which function
you call. Besides, if we have a function for BIBD or a function for OA
graphs we can add information there about their parameters about strongl
regular graphs, and it would have no meaning to add this in a much more
general function handling intersection graph.
Besides, some people who read your web page and who may want to create the
strongly regular graphs you mention may have absolutely no interest in
knowing how they are built, and they may not know even what a design is. I
am not just talking, a colleague of mine who could not care less about
designs wanted me to implement the graphs of some generalized triangles
just the other day as well as other things, and she it typically of this
type : she wants to work on the graph, but she is not sufficiently
interested in the subject to try to learn what an OA is and how they can
be built.
Besides, we may want n the future to build an internal database of
strongly regular graphs in Sage, and it is interesting for us to know that
the functions only have to be fed with integers and not wit something more
complicated like OA that we should take from somewhere else. It is better
if all functions expect the same kind of arguments.
--------
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/16370#comment:33>
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