Consider the following directed graph: Which of the following is/are correct…

Final conclusion: The only correct statement is that the graph does not have a topological order.

Reason:

• Presence of directed cycles prevents a topological ordering. A topological order exists only for directed acyclic graphs (DAGs). In this graph, following the directed edges around any small directed square brings you back to the starting vertex, so a directed cycle exists.

• Depth-first search edge classification depends on the neighbor visitation order. The exact number of back edges cannot be determined from the picture alone without specifying how neighbors are visited; each directed cycle contributes at least one back edge in some DFS orders, but the total count may vary.

• There are strongly connected components: nodes on the same directed cycle are mutually reachable, so they form nontrivial strongly connected components. Therefore the claim that there are no strongly connected components is false.

• The graph is not strongly connected as a whole, so it is not true that for every pair of vertices u and v there is a directed path from u to v. Edge directions restrict reachability between some vertices.

Therefore the correct answer is: the graph does not have a topological order, because directed cycles are present.