Given $|V|=4$ and $|E|=3$, how many distinct directed acyclic graphs can be formed? Isomorphic graphs should be counted as one.
- There is one where three periphery nodes point to a central node.
- There is a central node pointing to three periphery nodes.
- There are two variants of these two classes: one where two edges point out, and another where two edges point in.
- There is a linear graph $A\to B\to C\to D$.
Is these 5 classes all? How to solve this problem for a general graph? Incorporating acyclic property seems tough.