Last Updated:
4/1/10 10:16 AM
CSE 2011
Prof. J. Elder
- 91 -
DAGs and Topological Ordering
±
A directed acyclic graph (DAG) is a
digraph that has no directed cycles
±
A topological ordering of a digraph
is a numbering
v
1
, …, v
n
of the vertices such that for every
edge
(
v
i
, v
j
)
, we have
i
<
j
±
Example: in a task scheduling
digraph, a topological ordering is a
task sequence that satisfies the
precedence constraints
Theorem
A digraph admits a topological
ordering if and only if it is a DAG
B
A
D
C
E
DAG
G
B
A
D
C
E
Topological
ordering of
G
v
1
v
2
v
3
v
4
v
5

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*