How to prevent cycles in DAG graph?

[nikzanda]

My goal is to have a graph with one or more initial vertex and the nodes cannot be connected to the previous ones.

Here are some screenshots showing what I want. I have circled the starting edge in blue, the green tick is where node can connect and the red x is where node should not connect.

Also your example not working:

[bliberi]

I would like to do the same thing, has anyone achieved to prevent this?