1. DAGs
Longin Jan Latecki

2. DAGs In mathematics and computer science,
a directed acyclic graph (DAG), is a directed graph 
with no directed cycles.
That is, it is formed by a collection of vertices 
and directed edges, each edge connecting one vertex
to another, such that there is no way to start at some vertex v 
and follow a sequence of edges
that eventually loops back to v again.
DAGs may be used to model many different kinds of information.
The reachability relation in a DAG forms a partial order,
and any finite partial order may be represented
by a DAG using reachability.

3. Topological Sorting
A total ordering is said to be compatible with the partial ordering R if a b whenever a R b. Constructing a total ordering from a partial ordering is called topological sorting.

4. Topological Sorting

5. If there is an edge from v to w, then v precedes w in the sequential listing.1 2 3 4 5 6 7 8 9 9 6 3 4 8 2 5 1 7