[Nauty-list] Processing automorphism groups

Brendan McKay bdm at cs.anu.edu.au
Thu May 21 15:07:09 EST 2009


Hi, The number of isomorphs of an n-vertex graph is n! divided
by the automorphism group size.  nauty provides the latter in 
the stats argument.

If that isn't enough information, feel free to ask again.

Brendan.

* Demian Lessa <demian at lessa.org> [090521 09:48]:
> Hi,
> 
> I recently started a project that has a number of requirements, most of 
> which NAUTY satisfies out-of-the-box. There are a few things that I've 
> not been able to crack yet by reading the NUG and the source code. 
> 
> For instance,
> 
>   Is it possible to determine the number (count) of isomorphs of each
>   graph output by geng? I have looked at the statistics, the examples 
>   in NUG and the nautyexX.c files, to no avail. Am I missing something
>   very obvious?
> 
>   I would like to output this count for each graph in a custom 
>   OUTPROC routine that calls geng as follows:
> 
>     Graph 1, order 3, 1 isomorph.
>     00
>     0
> 
>     Graph 2, order 3, 3 isomorphs.
>     00
>     1
> 
>     Graph 3, order 3, 3 isomorphs.
>     01
>     1
> 
>     Graph 4, order 3, 1 isomorph.
>     11
>     1
> 
>   Note that this is the output from 'geng -lv 3 | listg -at' to 
>   which I added the isomorphism information.
> 
> Thank you!
> 
> Demian Lessa
> 
> 
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