Is there a name for a tree like graph, where nodes can have multiple parents, but still from only 1 level above

Question

Is there a name for a tree like graph, where nodes can have multiple parents, but still from only 1 level above.

Therefore the graph is directed and acyclic, but it has other constraints as well.

This will also mean that, all paths from any particular node back to the root are the same length.

Answer 1

I believe that this is called a layered graph. A graph of this sort is a graph where you can split the nodes into groups L₁, L₂, ..., L_n such that each edge (u, v) goes from some layer L_i to a second layer L_i+1.

Hope this helps!