# Number of non-isomorphic k-partite graphs.

There is a set of vertices and it is divided into $$k$$ independent sets. The cardinalities of these sets are following: $$a_{1},a_{2},...,a_{k}$$

How many non-isomorphic graphs determined on these sets are there?

I hope that someone will help me.

Regards.

• Where does this problem come from? The answer is, as far as I know, not known even for bi-partite graphs.. See for example math.stackexchange.com/questions/2321657/… – N. S. Sep 20 at 18:51
• The question is easy if you ask for the number of different labeled such graphs, but "isomorphic" makes it very hard. – N. S. Sep 20 at 18:52
• This MSE link treats the case of non-isomorphic bipartite graphs. – Marko Riedel Sep 21 at 14:44