Given a directed graph with 3 nodes, where order of nodes does not matter, how many graphs are possible?

Question

No nodes have self referencing arrows.

I tried solving on paper and got 14 graphs.

2 with 2 arrows, 4 with 3 arrows, 5 with 4 arrows, and 2 with 5 arrows, and 1 with 6 arrows.

With 2 arrows: 1 points to 2 points to 3. 1 points to 2 and 3.

With 3 arrows: 1 points to 2 and 3, and 2 points to 3. 1 points to 2 points to 3 points to 2. 1 points to 2 points to 3 points to 1.

With 4 arrows: 1 points to 3 points to 1 points to 2 points to 3. 1 points to 2 points to 1 points to 3, 2 points to 3. 1 points to 2 points to 3 points to 2, 1 points to 3. 1 points to 2 points to 3 points to 2, 3 points to 1. 1 points to 2 points to 3 points to 2 points to 1.

With 5 arrows: 1 points to 2 points to 3 points to 1 points 3, 2 points to 1. 1 points to 2 points to 3 points to 1 points to 3, 2 points to 3.

With 6 arrows: 1, 2, and 3 all point at each other.

Is this right? If not, is there a good source for finding the answer?

And finally, is there a textbook or source that goes into this? I tried looking for one, but the free graph theory textbooks I found don't cover this.

Answer 1

Here are the graphs:

With zero edges:

With one edge:

With two edges:

With three edges:

Done!