#16370: OA(k,n) strongly regular graphs
-------------------------+-------------------------------------------------
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: | 90a72bd39d74c24cb548e5b7dc5995c67ac386f8
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/16370 |
Dependencies: |
-------------------------+-------------------------------------------------
Comment (by ncohen):
Yo !
> So, what is the point of the ticket if we can already do
> {{{
> sage: g = Graph([map(Set, designs.transversal_design(3,7)), lambda x,y :
x&y])
> }}}
Several points :
1) To say that these graphs are stronly regular, and to give them a name
such that a guy looking at Brouwer's table can build them here
2) The implementation is better : the syntax above checks whether any two
sets have a non-empty intersection, which is not what this code does
3) It may later be useful to have a large collection of constructors for
"interesting" graphs (and strongly regular graphs ARE interesting) to
check conjectures and stuff
4) We both agree that we needs a `graphs.IntersectionGraph` function
because the syntax above is not very natural, don't tell me now that user
should find it by themselves `:-P`
> Moreover, the graph you obtain is also strongly regular with BIBD input
> {{{
> sage: BIBD = designs.BalancedIncompleteBlockDesign(31,6)
> sage: V = map(Set, BIBD.blocks())
> sage: G = Graph([V, lambda x,y: x&y])
> sage: G.is_strongly_regular(parameters=True)
> (31, 32, 31, -1)
> }}}
Err... Well, this is actually a bug report. The parameters must always be
positive. Will look at it right now.
> I would rather add those examples to the documentation (of both designs
and graphs). We could possibly add them to the documentation of the not
yet existing `graphs.IntersectionGraph`.
Tell me if my answers above convinced you.
Nathann
--
Ticket URL: <http://trac.sagemath.org/ticket/16370#comment:17>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
