Question

Which is a valid topological sort of the graph below? (Select all that apply.) Group of answer choices

a) V1 V3 V4 V6
b) V0 V2 V5
c) V0 V1 V3 V2 V4 V6 V5
d) V0 V2 V1 V4 V3 V5 V6

Answer 1

The valid topological sorts of the given graph are: c) V0 V1 V3 V2 V4 V6 V5 d) V0 V2 V1 V4 V3 V5 V6

Step-by-step explanation:

In a topological sort, the vertices of a directed acyclic graph (DAG) are linearly ordered such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering.

To determine the valid topological sorts of the given graph, we can start by identifying the vertices with no incoming edges. In this case, V0 has no incoming edges, so it must appear first in the topological sort. Then, we remove V0 and its outgoing edges from the graph and repeat the process until all vertices are included in the topological sort.

Starting with V0, the valid topological sorts are: c) V0 V1 V3 V2 V4 V6 V5 d) V0 V2 V1 V4 V3 V5 V6

Therefore, both options c and d are valid topological sorts for the given graph.

So correct option is c) V0 V1 V3 V2 V4 V6 V5 d) V0 V2 V1 V4 V3 V5 V6