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GATE DA 2024 Q51: Valid topological orderings of a DAG

Question

Consider the directed acyclic graph (DAG) below:

DAG with edges P to Q, R to Q, Q to S, Q to V, S to U and V to T
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Which of the following is/are valid vertex orderings that can be obtained from a topological sort of the DAG?

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Answer: B, D (official GATE 2024 final answer key)

Concept used: In a topological order every edge goes from an earlier vertex to a later one.

First step: Edges: P→Q, R→Q, Q→S, Q→V, S→U, V→T. Any ordering with Q before R, or T before V, is invalid.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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