[Nauty] How to apply automorphisms?

[Aisha Fenton]

Hi,
I'm currently using nauty to test a pair of graphs for an isomorphism. 
However, now I have a requirement that once nauty has found a canonic 
labeling for two isomorphic graphs (G, H)  I want to test if vertices v 
in V(G) are ever mapped to y in V(H) under some automorphism.

That is, I have vertex boundary defined on each G and H. Once I have 
found that G and H are isomorphic, I want to see if the boundary on G 
is mappable to H (for some automorphism)

 From the documentation the only way I could see was to parse the 
automorphism output file, and then try each cycle - since I'm dealing 
with hundreds of thousands of graphs, this method seemed like it 
wouldn't be fast enough for me.

Also a newbie question. I'm not that versed in group theory, so I'd 
really appreciate it if someone could give me a quick run down of how 
I'm to interrupt the output automorphisms (I only need to know if 
vertex x ever maps to vertex y). From my very basic group theory 
knowledge, I was expecting the examples in the documentation of the 
output automorphisms, to contain something like a rotation cycle 
(01,2,3,4,5,6), but they don't?


Thanks heaps,
Aisha