#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 knsam):
I think it would be misleading to call it a Steiner design graph, as an
incidence system can give rise to a graph in atleast three different ways:
- Levi Graph: this is a bipartite graph whose vertices are points and
lines in the system and adjacency is the incidence of the incidence
system.
- Adjacency graph: the points are the vertices; two vertices are adjacent
if they are incident in a common line.
- Block Intersection graph: the vertices are blocks of the system and two
vertices are adjacent if they meet in some number of points.
As I indicated above, it is common to call the graphs that we are talking
about as Block intersection graphs.
A quasi-symmetric design is a 2-design with atmost two block intersection
numbers. Those with only one block intersection number are the square (or
symmetric) 2-designs. One can solve the equations one obtains by using
Fischer's variance counting to get the parameters in this case.
Curiously, petersen graph is the block intersection graph of the 2-design
2-(6, 3, 2) (this is a quasi-symmetric design: any two blocks meet in 0
points or 1 point) where you define adjacency among blocks as "being
disjoint". See [http://sina.sharif.edu/~emahmood/papers/MR1147979.PDF
here].
Hope this is helpful.
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Ticket URL: <http://trac.sagemath.org/ticket/16370#comment:21>
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