# How many complete directed graphs are there up to Isomorphism?

How many tournament graphs are there up to Isomorphism?

Context: I am examining properties of complete directed graphs and so am trying to enumerate them on my simulation. I would like to know precisely how intractable this is.

• oeis.org/A000568 – Mike Earnest Mar 21 at 23:15
• Probably really complicated as Harary initially gave an incorrect calculation – Jorge Fernández Hidalgo Mar 21 at 23:20
• @MikeEarnest No, A000568 is the number of tournaments (oriented complete graphs) of order $n$. As far as I know, there is only one complete digraph of order $n$, up to isomorphism. Each pair of vertices is joined by an arc in each direction, and there is a loop at each vertex. – bof Mar 22 at 5:50
• Up to isomorphism, for each $n$ there is just one complete directed graph of order $n$. Are you sure it's complete directed graphs you're interested in, and not tournaments? – bof Mar 22 at 5:56