Consider the dag with set of nodes V = {V1, V2, V3, V4, V5, V6, V7} and set of edges {(V1,V2), (V1,V3), (V1,V4), (V2,V5), (V3,V5), (V3,V6), (V4,V6), (V5,V7), (V6,V7)}. Which of the following node sequences are topologically sorted? Group of answer choices V1, V3, V4, V6, V2, V5, V7 V1, V3, V2, V6, V4, V5, V7 V1, V3, V4, V5, V2, V6, V7 V1, V2, V5, V3, V4, V6, V7 V1, V4, V3, V2, V6, V5, V7
Question
Consider the dag with set of nodes V = {V1, V2, V3, V4, V5, V6, V7} and set of edges {(V1,V2), (V1,V3), (V1,V4), (V2,V5), (V3,V5), (V3,V6), (V4,V6), (V5,V7), (V6,V7)}. Which of the following node sequences are topologically sorted? Group of answer choices
V1, V3, V4, V6, V2, V5, V7
V1, V3, V2, V6, V4, V5, V7
V1, V3, V4, V5, V2, V6, V7
V1, V2, V5, V3, V4, V6, V7
V1, V4, V3, V2, V6, V5, V7
Solution
The correct answer is: V1, V2, V5, V3, V4, V6, V7
Here's why:
A topological sort of a directed acyclic graph (DAG) is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering.
Let's check each option:
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V1, V3, V4, V6, V2, V5, V7: This is not a valid topological sort because V2 comes after V3 and V4, but there is a directed edge from V1 to V2.
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V1, V3, V2, V6, V4, V5, V7: This is not a valid topological sort because V4 comes after V2, but there is a directed edge from V1 to V4.
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V1, V3, V4, V5, V2, V6, V7: This is not a valid topological sort because V2 comes after V5, but there is a directed edge from V2 to V5.
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V1, V2, V5, V3, V4, V6, V7: This is a valid topological sort. All directed edges go from a vertex to a vertex later in the sequence.
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V1, V4, V3, V2, V6, V5, V7: This is not a valid topological sort because V2 comes after V3, but there is a directed edge from V1 to V2.
Therefore, the only valid topological sort is V1, V2, V5, V3, V4, V6, V7.
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