# Term for a "rooted" directional graph?

Consider an acyclic directed graph in which a traversal from any node in the graph must eventually end at some terminal node R. Borrowing from tree-based vocabulary, I would tend call this the "root" of the graph, since all traversals eventually terminate there. However, the term "rooted graph" seems to already be in use for something else.

Is there a term I can use to describe this property? The best way I can describe the graph at present is a "multi-parented directed tree" -- all nodes point toward the root, but, unlike a directed tree, nodes may have more than one parent. I don't like this terminology, though, as it seems like an abuse of the term "tree".

I considered "hierarchical graph", but a node can have more than one outgoing vertex, so I think that may disqualify it from being hierarchical.

• If it's a tree, call such a directed tree with each edge oriented towards the root an inverse pine. (A pine is a tree with every edge is oriented away from the root.) If it's not a tree, then I have no idea. Jul 25, 2012 at 20:48
• @ZsbánAmbrus: Do you have a source for the term "pine"? Jul 25, 2012 at 23:13
• @JeffE: Hmm, can I change my reply then? Call such a tree an inverse arborescence, the source being Lovász, Combinatorial Problems and Exercises. Jul 26, 2012 at 8:11
• A rooted graph is usually identified with a directed graph (with the root being the 'source'). It is perfectly reasonable to treat the root as the 'sink' instead. Sep 9, 2019 at 8:46