[Nauty-list] elements of the automorphism group

[Juan Felipe Carrasquilla]

Dear All,

I am a newcomer in the list. I am trying to use nauty to link it to a
quantum monte carlo code to generate the all the symmetries of the
lattices we deal with. The lattices ( and the boundary conditions as well)
can be pictured using graphs so this is why we think nauty could be very
useful.

Nauty provides the information of the automorphism group of a graph in the
form of a set of generators, the size of the group, and the orbits of the
group. For our application, it would be desirable to have, instead of the
generators and the orbit, the full group components. I have little
background in group theory but as far as I understand I can generate all
the components of the group by using the generating set X and a finite
product of elements of it and their inverses. What I do not know is how to
generate those combinations of the elements of the generating set with the
information provided by nauty, namely the generating set, the orbits of
the groups and the size of the group.

Is nauty able to provide the information of the automorphism group by
listing all the elements?

If not, is there a systematic way to generate the elements  with the
information provided by nauty? (this might not be a good question for this
list but if anyone can help me I would be grateful)

Thanking you,

Juan


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