[Nauty] ?

[Lluís Alemany Puig]

Hello all,

I thought this may be of your interest, now that we know Nauty does not 
have such algorithms.

The Linear Arrangement Library (which is free software -- free as in 
freedom) contains algorithms to generate all rooted trees with n nodes 
(labelled and unlabelled).

  * Link to github:
    https://github.com/LAL-project/linear-arrangement-library
  * Official webpage: https://cqllab.upc.edu/lal/

Links to C++ documentation to generate trees:

  * all /labelled/ rooted trees (of n vertices):
    https://cqllab.upc.edu/lal/cppdocs/latest/html/classlal_1_1generate_1_1all__lab__rooted__trees.html#details
  * all /unlabelled/ rooted trees (of n vertices):
    https://cqllab.upc.edu/lal/cppdocs/latest/html/classlal_1_1generate_1_1all__ulab__rooted__trees.html#details

Links to C++ documentation to select trees uniformly at random:

  * uniformly random /labelled/ rooted trees (of n vertices):
    https://cqllab.upc.edu/lal/cppdocs/latest/html/classlal_1_1generate_1_1rand__lab__rooted__trees.html#details
  * uniformly random /unlabelled/ rooted trees (of n vertices):
    https://cqllab.upc.edu/lal/cppdocs/latest/html/classlal_1_1generate_1_1rand__ulab__rooted__trees.html#details

There are also the "free" variants of these algorithms, i.e., algorithms 
to generate labelled/unlabelled free trees, and select 
labelled/unlabelled free trees uniformly at random.

You can use the Linear Arrangement Library with C++ and/or python.

Hope you find this useful,

Lluís

On 15/07/2023 09:31, Brendan McKay wrote:
> Hi Keith,  No I don't have one of those at the moment.  Brendan.
>
> On 15/7/2023 4:52 pm, Keith Paton wrote:
>> hello,
>>
>> I am writing an algorithm to generate all the rooted trees with n 
>> nodes. Does nauty have one?
>>
>> Many thanks,
>>
>> Keith
>>
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