Clarification of Graph Terminology

Question

Hi guys, I'm working on a homework question and I've got the answer, but I'm not sure if the terminology I'm using is correct and I was hoping if someone can clarify. Here's the situation:

I have a graph in the shape of a rectangle of size M x N. The node at (0, 0) has no incoming edges. All other nodes have incoming edges from the north, northwest, and west, unless they are on the top or left-most side, in which case the diagonal incoming edge does not exist and either the edge from the west or north does not exist.

So if starting at node (0, 0) and following any path to its finish, it will end at node (m, n). I am now asked to define what type of graph this is. Is this a directed acyclic graph?

Answer 1

Yep, it is, because each edge has a direction (hence directed) and there are no cycles - once you leave any node, there's no way to get back to it by following the edges of the graph (hence acyclic). See http://en.wikipedia.org/wiki/Directed_acyclic_graph for more info.