[Nauty-list] Re: A question on nauty

[Brendan McKay]

Sorry for the delay in replying.  Nauty already takes advantage
of properties like this, but you might be able to help it by
adding extra edges to the graph in places that are combinatorially
determined.  That would assist nauty in propagating the effect of
a choice from one place to the whole graph.  In all cases, prefer
to use vertex colouring and undirected edges in preference to
directed edges, if possible.

Brendan.


* Mathieu Dut ur <Mathieu.Dutour at ens.fr> [070613 23:46]:
> Dear all,
> 
> I have a class of graph, which has the following property:
> --S is a subset of the vertex set.
> --If phi is an automorphism, then phi is is determined by its
>   restriction to S.
> 
> Can thie property be used, in principle, to speed up automorphism
> search?
> 
> The context is determination of automorphism group of lattices of
> R^n or in other words of matrices P in GLn(Z) such that PA P^t=A
> with A positive definite.
> The method is to select a family of vectors (v_i)_{1 <= i <= M},
> which we know to be invariant by the automorphism group and build
> the edge colored graph v_i A v_j^t.
> There is a classic software in this field, CARAT, which does the
> job but in some cases nauty is superior to it despite the layers
> of translation and I am searching for a way to combine both
> strengths.
> 
> Thank you in advance for any help.
> Best,
> 
>   Mathieu
> 
> -- 
> Mathieu Dutour Sikiric		Researcher in Mathematics
> Telephone:.(+385)1 4571 237	and Computer Science
> Cell Phone: (+385)9 19 36 30 80	Laboratory of satellite oceanography
> E-mail: Mathieu.Dutour at ens.fr	Rudjer Boskovic Institute
> http://www.liga.ens.fr/~dutour	Zagreb Croatia
> skype name: mathieudutour