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
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.)