What is the name of this type of directed acyclic graph?

Question

Perhaps it isnt even a DAG, but as its naming im after i wasnt sure what title to give this...

What is the name of a data structure where every node can only have 0 or 1 paths INTO it? Strictly, is this a tree?

Thanks

Answer 1

It's a directed tree. Plain trees as such are undirected.

Your constraint isn't precisely how trees are defined (the definition of a tree is that any two vertices are connected by no more than one path), but it does constrain your graph to be a valid directed tree. (Unless you want to employ weird usages of 'directed tree' that require a uniform tropism, which I can't say interests me.)

Answer 2

Are there any other constraints? From only the one you've given I can construct a graph that is not a tree.

A -> B -> A

If you add the constraint that the graph is acyclic, then it would be a tree.