GATE CS 2014 Set 1 — Question 23
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Algorithms → Graph Algorithms → Topological Sort
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Question
Consider the directed graph given below.
Which one of the following is TRUE?
Correct answer
(C) Both PSRQ and SPRQ are topological orderings.
Solution
A topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge from vertex to vertex , comes before in the ordering. A topological ordering is possible if and only if the graph has no directed cycles (i.e., it is a Directed Acyclic Graph or DAG).Let's analyze the given graph for cycles:
- There is an edge
P → Q. - There is an edge
Q → S. - There is an edge
S → P.
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