Topological Sorting Concepts and Problems

The video tutorial introduces topological sorting, a method for ordering vertices in a directed acyclic graph (DAG) such that for every directed edge UV, vertex U comes before V. It explains the necessary conditions for topological sorting, emphasizing that the graph must be directed and acyclic. The tutorial provides a step-by-step method to find topological sorting using in-degree and out-degree concepts, illustrated with examples. It also demonstrates why topological sorting is not possible in graphs containing cycles. The video concludes with additional examples and reiterates the possibility of multiple topological orderings in a DAG.

What is the primary focus of topological sorting?

• Arranging vertices in a linear order

• Determining the minimum spanning tree

• Finding the shortest path

• Calculating the maximum flow

Which type of graph is required for topological sorting?

• Weighted graph

• Directed cyclic graph

• Directed acyclic graph

• Undirected graph

What happens if a graph contains a cycle?

• The graph becomes undirected

• The graph becomes weighted

• Topological sorting is still possible

• Topological sorting is not possible

In topological sorting, which vertex is chosen first?

• Vertex with the highest degree

• Vertex with the lowest degree

• Vertex with in-degree zero

• Vertex with out-degree zero

What is the in-degree of a vertex?

• Number of vertices connected to it

• Total number of edges in the graph

• Number of edges coming into the vertex

• Number of edges going out from the vertex

Why can't a graph with a cycle have a topological ordering?

• Because it has too many vertices

• Because it has too many edges

• Because there will be no vertex with in-degree zero

• Because it is undirected

What is the result of deleting a vertex with in-degree zero?

• The in-degrees of affected vertices are updated

• The graph becomes undirected

• The in-degrees of other vertices remain unchanged

• The graph becomes cyclic

In the example with a cycle, what was the issue encountered?

• The graph was weighted

• The graph was undirected

• No vertex had in-degree zero

• All vertices had in-degree zero

How many topological orderings can a directed acyclic graph have?

• Only one

• None

• At least one, possibly more

• Exactly two

What is the first step in finding a topological sort?

• Calculate the shortest path

• Find the in-degree of each vertex

• Convert the graph to undirected

• Identify all cycles