For certain applications it is convenient to deal with graphs that contain no cycles. For example, a tree (see Chapter ) is a special kind of graph that contains no cycles.
Definition (Directed Acyclic Graph (DAG))A directed, acyclic graph is a directed graph that contains no cycles.
Obviously, all trees are DAGs. However, not all DAGs are trees. For example consider the two directed, acyclic graphs, and , shown in Figure . Clearly is a tree but is not.
Figure: Two Directed, Acyclic Graphs