I know the following problem is famous:

- For a given degree sequence $L$ that is graphic, find an (efficient) algorithm to generate all of the nonisomorphic realizations of $L$.

This algorithm is sometimes helpful when we gather experimental evidence for conjectures (or as part of a proof).

There are many such articles, but the implementation of algorithms seems very few. I recently saw the following article, which provides the software `gradpart`

.

- Grüner T, Laue R, Meringer M. Algorithms for group actions applied to graph generation[C]//Groups and Computation II. AMS, 1997, 28: 113-123.
- http://www.mathe2.uni-bayreuth.de/thomas_g/gradpart.html

But because the code was written around 1995, it is difficult for today's compilers to make it (due to the constant updating of the *C++* standard).

I read the author's description and it looks like it can quickly generate all nonisomorphic graphs by a given degree sequence.

In this example you can see a degree-partition with 50 vertices. Here we have 2 vertices of degree 1, 10 vertices of degree 2, 8 vertices of degree 3,... . Because of the use of the homomorphism-principle, during the generation we may obtain situations, where the operating group is trivial. So we get the possibility to describe large sets of pairwise non-isomorphic solutions implicitly. In this way in the shown example, we computed

34824038400 graphsin about25 secondsand are also able to store these graphs with a very small amount of space.

I know `nauty`

is great, but it seems not to offer this feature (except for generating regular graphs).
Especially for cases with a slightly higher number of vertices (e.g. more than 15 vertices)

It is not clear if there is an alternative math software, or if there is a later version of `gradpart`

for using it today. If there is an updated version of the software `gradpart`

, we would love to see it play a role in the discovery of theorems.

`make Gradpart`

in order not to build the GUI. That's a relief. However, the C++ dialect is very, very old, and apparently the code does not even use C++ STL (indeed, STL only appeared in 1994, and this code dates back to 1996). Instead there are home-made templates (in *.t files). $\endgroup$3more comments