The document discusses topological sorting of directed acyclic graphs (DAGs). It explains that topological sorting is a linear ordering of vertices in a DAG such that all directed edges point from earlier to later vertices. The document provides an algorithm to find the topological ordering of a DAG by computing in-degrees of vertices and adding those with zero in-degree to a queue. It also lists applications of topological sorting like building systems and advanced packaging tools.

1. Bangladesh Army University of Science and Technology, Saidpur
Submitted By: Submitted To:
S.M. Fahim Shahriar Md. Shajalal
160101051 Designation: Lecturer
Sec B

2. Topological Sorting

3. Idea:
For a directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every edge (u,v),
vertex u comes before v in the ordering.
Topological Sorting

4. Idea:
For a directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every edge (u,v),
vertex u comes before v in the ordering.
Topological Sorting
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5. Idea:
For a directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every edge (u,v),
vertex u comes before v in the ordering.
For a DAG
Topological sort is not unique.
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Topological Sorting
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6. Topological Sorting
APPLICATIONS:
• Build Systems
• Advanced-Packaging Tool

7. Algorithm’s
Algorithm:
Steps involved in finding the topological ordering of a DAG:
Step-1: Compute in-degree (number of incoming edges) for each of the vertex present in the
DAG and initialize the count of visited nodes as 0.
Step-2: Pick all the vertices with in-degree as 0 and add them into a queue (Enqueue operati
on)
Step-3: Remove a vertex from the queue (Dequeue operation) and then.
Increment count of visited nodes by 1.
Decrease in-degree by 1 for all its neighboring nodes.
If in-degree of a neighboring nodes is reduced to zero, then add it to the queue.
Step 4: Repeat Step 3 until the queue is empty.
Step 5: If count of visited nodes is not equal to the number of nodes in the graph then the top
ological sort is not possible for the given graph

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30. Thank You