[Nauty] What are the differences between using and not using the -t option in labelg for canonical graph labeling?

[lczhangmath]

Dear Brendan,

Thank you! I see now. I saw many software, like sage/Mathematica, function concerning canonical labeling all use traces(-t). So I thought canonical  labeling is always unique.

Thank you again!

Best wishes,
Licheng.

---- Replied Message ----
| From | Brendan McKay via Nauty<nauty at anu.edu.au> |
| Date | 07/21/2024 22:10 |
| To | nauty<nauty at anu.edu.au> |
| Subject | Re: [Nauty] What are the differences between using and not using the -t option in labelg for canonical graph labeling? |
labelg always makes a canonical labelling, but what "canonical" means
depends on the options.
   -t, -S, -f, -i, -I, -K all change the meaning.

In order to compare some family of graphs, you have to use the same
options for all of them.

Brendan.


On 21/7/2024 11:30 pm, lczhangmath via Nauty wrote:
> Hello, everyone,
>
>
> I noticed the option -t in labelg. I would like to ask, if I don't use the -t option, will the obtained labels still be canonical? In other words, if I want to get the canonical labeling of a graph, do I have to use the -t option? I noticed that when I don't use the -t option for canonical graph labeling, the graph's labels also change. So, what is labelg doing at this time? Do the obtained labels have some special meaning?
>
>
>   echo 'E{EG' |showg
>
>
>
>
> Graph 1, order 6.
>    0 : 1 2 3 5;
>    1 : 0 2;
>    2 : 0 1;
>    3 : 0 4;
>    4 : 3 5;
>    5 : 0 4;
>
>
>
>
> echo 'E{EG' |labelg |showg
>
>
> Graph 1, order 6.
>    0 : 4 5;
>    1 : 4 5;
>    2 : 3 5;
>    3 : 2 5;
>    4 : 0 1;
>    5 : 0 1 2 3;
>
>
>
>
> Use  labelg  -t:
> echo 'E{EG' |labelg  -t|showg
>
>
> Graph 1, order 6.
>    0 : 3 4;
>    1 : 2 5;
>    2 : 1 5;
>    3 : 0 5;
>    4 : 0 5;
>    5 : 1 2 3 4;
>
>
> Best wishes,
> Licheng
> _______________________________________________
> Nauty mailing list
> Nauty at anu.edu.au
> https://mailman.anu.edu.au/mailman/listinfo/nauty

_______________________________________________
Nauty mailing list
Nauty at anu.edu.au
https://mailman.anu.edu.au/mailman/listinfo/nauty