#18948: Strongly Regular Graphs database
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Reporter: ncohen | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: graph theory | Keywords:
Merged in: | Authors: Nathann Cohen
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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This ticket implements a new module names `strongly_regular_db` that lets
us build one example of strongly regular graph, given four integer
parametes (v,k,lambda,mu).
It uses Andries Brouwer's database to return more meaningful non-existence
results, and help us find which constructions are missing from the
database.
With a bit of luck (and time, and work) it would be great if we could
reproduce all SRG that are known to exist!
The module has a simple structure:
has a simple structure:
- A `seems_feasible(v,k,l,mu)` function that performs the basic artihmetic
checks to figure out if `(v,k,l,mu)` is realizable. The
'apparently_feasible_parameters(n)` returns the lists of all parameters
that
pass these tests for v<n. When n=1301, the set of parameters it returns
is
precisely those that appear on your database (this is checked in the
code).
- Several functions (is_paley, is_johnson, ...) test if a given set of
parameters (v,k,l,mu) can be realized with a graph of the corresponding
family
(a Paley graph, a Johnson graph, ...). If they can, they return the
parameters
of that graph so that it can be built easily.
- The main function `strongly_regular_graph` can be called in two ways:
- `strongly_regular_graph(v,k,l,mu,existence=True)` answers True if such
a
graph is known to exists, False if it is known to be infeasible, and
Unknown
otherwise.
- `strongly_regular_graph(v,k,l,mu)` attempts to build and return the
requested graph, and returns a meaningful exception if it cannot.
This branch also updates the package 'graphs', which now ships the
database in json format.
Nathann
--
Ticket URL: <http://trac.sagemath.org/ticket/18948>
Sage <http://www.sagemath.org>
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