#19018: More SRGs using Regular Symmetric Hadamard matric with Constant Diagonal
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.9
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | 6893ad1163b8c636fe4f54e3ff838ccad85f4d5b
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/19018 |
Dependencies: |
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Comment (by dimpase):
Replying to [comment:16 ncohen]:
> > I do not like how (100, 44, 18, 20)-srg and (100, 45, 20, 20) are
specified. Why don't you present them as Cayley graphs?
>
> Because it takes several minutes to build it,
huh? Here is an experiment with GAP, which is almost instant to run:
{{{
gap> g:=CyclicGroup(100);
<pc group of size 100 with 4 generators>
gap> l:=List([1..45], x->Random(g));
[ f2*f3, f2*f3^4*f4^2, f1*f3^4*f4^2, f1*f4^4, f2*f3^3*f4^4, f2*f3^3*f4^3,
f2*f4^2, f4, f2*f3^3*f4^3,
f1*f4, f1*f4^3, f2*f3^4, f1*f2*f4^4, f1*f3^4*f4^4, f3^3, f1*f3^3*f4^4,
f1*f3^3*f4, f2*f3^4*f4^4,
f1*f3^2, f3^3*f4^4, f2*f3^2*f4, f1*f3^2*f4^3, f2*f3^4, f2*f3^3*f4^2,
f2*f3^3*f4, f1*f3^3*f4, f3*f4,
f2*f3^3*f4^4, f3^2*f4, f1*f2*f3^4*f4^4, f3^4*f4^4, f1*f3^3*f4,
f1*f3^4*f4^2, f1*f3^2*f4^2,
f2*f3^4*f4^3, f1*f2*f3, f3, f1*f3^4, f2*f4^4, f1*f3^2, f2*f3^3, f3^2*f4,
f3*f4^4, f2*f3^3*f4^2, f4^3 ]
gap> LoadPackage("grape");
true
gap> G:=CayleyGraph(g,l);
rec(
adjacencies :=
[ [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 20, 21, 22, 23, 25,
28, 32, 33, 34, 35, 37, 41,
43, 46, 47, 48, 50, 51, 52, 54, 55, 59, 60, 62, 63, 64, 67, 70,
71, 72, 74, 75, 76, 80, 83,
84, 86, 87, 90, 92, 93, 94, 95, 96, 98, 99, 100 ] ],
group := <permutation group of size 100 with 4 generators>, isGraph :=
true, isSimple := true,
names := [ <identity> of ..., f1, f2, f3, f4, f1*f2, f1*f3, f1*f4,
f2*f3, f2*f4, f3^2, f3*f4, f4^2,
f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3^2, f2*f3*f4,
f2*f4^2, f3^3, f3^2*f4,
f3*f4^2, f4^3, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^3,
f1*f3^2*f4, f1*f3*f4^2, f1*f4^3,
f2*f3^3, f2*f3^2*f4, f2*f3*f4^2, f2*f4^3, f3^4, f3^3*f4, f3^2*f4^2,
f3*f4^3, f4^4, f1*f2*f3^3,
f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3^4, f1*f3^3*f4,
f1*f3^2*f4^2, f1*f3*f4^3, f1*f4^4,
f2*f3^4, f2*f3^3*f4, f2*f3^2*f4^2, f2*f3*f4^3, f2*f4^4, f3^4*f4,
f3^3*f4^2, f3^2*f4^3, f3*f4^4,
f1*f2*f3^4, f1*f2*f3^3*f4, f1*f2*f3^2*f4^2, f1*f2*f3*f4^3,
f1*f2*f4^4, f1*f3^4*f4, f1*f3^3*f4^2,
f1*f3^2*f4^3, f1*f3*f4^4, f2*f3^4*f4, f2*f3^3*f4^2, f2*f3^2*f4^3,
f2*f3*f4^4, f3^4*f4^2,
f3^3*f4^3, f3^2*f4^4, f1*f2*f3^4*f4, f1*f2*f3^3*f4^2,
f1*f2*f3^2*f4^3, f1*f2*f3*f4^4,
f1*f3^4*f4^2, f1*f3^3*f4^3, f1*f3^2*f4^4, f2*f3^4*f4^2,
f2*f3^3*f4^3, f2*f3^2*f4^4, f3^4*f4^3,
f3^3*f4^4, f1*f2*f3^4*f4^2, f1*f2*f3^3*f4^3, f1*f2*f3^2*f4^4,
f1*f3^4*f4^3, f1*f3^3*f4^4,
f2*f3^4*f4^3, f2*f3^3*f4^4, f3^4*f4^4, f1*f2*f3^4*f4^3,
f1*f2*f3^3*f4^4, f1*f3^4*f4^4,
f2*f3^4*f4^4, f1*f2*f3^4*f4^4 ], order := 100, representatives := [
1 ],
schreierVector := [ -1, 1, 2, 3, 4, 2, 3, 4, 3, 4, 3, 4, 4, 3, 4, 3, 4,
4, 3, 4, 4, 3, 4, 4, 4, 3, 4,
4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4,
3, 4, 4, 4, 4, 4, 4, 4, 4,
3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4 ] )
}}}
in your case the group will be given by 3 permutation generators, but this
will only make it even faster.
> > Further, the paper you cite constructs several nonisomorphic examples
of these graphs, and you don't say which ones you give.
>
> I do not think that it matters. I just want one.
How hard is to say that in a comment that you used pds such-and-such for
group such-and-such?
--
Ticket URL: <http://trac.sagemath.org/ticket/19018#comment:18>
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