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

Let us analyze each statement based on standard graph theory and traversal properties:

1. Topological Order (Option A): A directed graph has a topological ordering if and only if it is a Directed Acyclic Graph (DAG). The given graph contains directed cycles (for example, the cycle formed by vertices in the grid). Since it contains at least one cycle, it is not a DAG, and therefore does not have a topological order. Hence, Option A is correct.

2. Back Edges in DFS (Option B): A depth-first traversal starting from vertex $S$ reaches all $16$ vertices. In any DFS tree of this graph, the DFS tree contains $15$ tree edges. Out of the remaining non-tree edges encountered during traversal, exactly $3$ directed edges point from a descendant to an ancestor, which classifies them as back edges (corresponding to the fundamental cycles). Thus, Option B is correct.

3. Strongly Connected Component (Option C): Every directed graph has at least one strongly connected component (SCC) (trivially, even single vertices are SCCs if there are no larger ones, and here non-trivial SCCs exist as well). Thus, the statement that the graph does not have an SCC is false. Hence, Option C is incorrect.

4. Strong Connectivity of the Entire Graph (Option D): For each pair of vertices $u$ and $v$ to have a directed path between them, the entire graph would need to be strongly connected. Since the graph is not strongly connected (for instance, the top-right vertices have no path back to $S$), this statement is false. Hence, Option D is incorrect.

Therefore, the correct options are A and B.