On Sun, Oct 23, 2016 at 9:05 AM, Paul Leopardi <paul.leopa...@gmail.com> wrote:
> Since asking the question "How should I determine if two strongly regular
> graphs are isomorphic?" I have made great progress in classifying Bent
> functions by their Cayley graphs.
> That is, up until now. I have found two graphs which I was (emprically)
> expecting to be isomorphic have different canonical labels.
>
> To reproduce:
> 1. Clone the python-refactor branch of penguian/Boolean-Cayley-graphs
> 2. Copy the attached Sage file test_isomorphism.sage to your cloned
> Boolean-Cayley-graphs directory.
> 3. In your cloned Boolean-Cayley-graphs directory, run sage and enter
> load("test_isomorphism.sage")
>
> You should see:
>
> sage: load("test_isomorphism.sage")
> Defining bent function f...
> f.algebraic_normal_form() == x0*x1*x6 + x0*x3 + x1*x4 + x2*x3*x6 + x2*x5 +
> x3*x4 + x4*x5*x6 + x6*x7
> Determining strongly regular graphs SG1 and SG2...
> Finding canonical labels CG1 and GG2...
> CG1 == CG2: False
> G1.is_isomorphic(G2): False
> SageCG1 == SageCG2: False
> SG1.stored_clique_polynomial == SG2.stored_clique_polynomial: True
> SG1.stored_clique_polynomial == 45056*t^9 + 780288*t^8 + 2998272*t^7 +
> 5505024*t^6 + 4816896*t^5 + 1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
> SG1.rank == SG2.rank: True
> SG1.rank == 16
> SG1.group_order == SG2.group_order: True
> SG1.group_order == 229376
> G1.automorphism_group().is_isomorphic(G2.automorphism_group()): True
> sage:
>
> This is saying that G1, the Cayley graph of f, and G2, the strongly regular
> graph obtained from the two-weight code derived from f, are not isomorphic,
> *but*
> G1 and G2 have the same clique polynomial, *and*
> G1 and G2 have isomorphic automorphism groups.
>
> Do you have any hints on how I can further diagnose what is really going on
> here? I suspect a bug in my own code rather than a bug in Sage or a true
> non-isomorphism, but at this stage I can't be sure.
> For example, I have not yet found nor devised a proof that G1 and G2 should
> be isomorphic, beyond observing that it is true for all the other cases I
> have examined so far.
>
> The code for cayley_graph() and for strongly_regular_graph() is in
> bent_function.py.
> The method strongly_regular_graph() depends on linear_code(), which is
> defined in boolean_function_improved.py, and is based on a simplified
> version of Ding III a) https://arxiv.org/abs/1503.06511I haven't looked at your code but are you comparing the SRG associated to the Boolean bent function and the graph associated to the incidence matrix of that graph? > Sorry I haven't yet fully documented my code. It is a work in progress. > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
