Which of the following is/are the results of the topological

Topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u, v) from vertex u to vertex v, u comes before v in the ordering.

Key precedence constraints visible in the graph:

• 8 comes before 7, and 7 comes before 6 (8 → 7 → 6).

• 0 comes before 1, before 5, and before 6 (0 → 1, 0 → 5, 0 → 6).

• 2 comes before 3, and 3 comes before 5 (2 → 3 → 5).

• Both 5 and 6 come before 4 (5 → 4 and 6 → 4).

• 6 comes before 9; 9 comes before 10, 11 and 12; and 11 comes before 12 (6 → 9 → {10, 11, 12}, 11 → 12).

Check each candidate ordering against these constraints:

• Sequence: 2, 8, 0, 7, 1, 3, 5, 6, 4, 9, 10, 11, 12 — All required precedences hold: 8 before 7 before 6; 0 before 1,5,6; 2 before 3 before 5; 5 and 6 before 4; and 6 before 9 then 10,11,12 with 11 before 12.

• Sequence: 2, 8, 7, 0, 6, 9, 11, 12, 10, 1, 3, 5, 4 — All required precedences hold: 8 → 7 → 6; 0 is before its successors; 2 → 3 → 5; 5 and 6 before 4; and 6 → 9 → 10/11/12 with 11 → 12.

• Sequence: 8, 2, 7, 0, 6, 9, 10, 11, 12, 1, 3, 5, 4 — All required precedences hold: 8 → 7 → 6; 0 before its successors; 2 → 3 → 5; 5 and 6 before 4; and 6 → 9 → 10/11/12 with 11 → 12.

Conclusion: Each listed sequence satisfies every directed edge constraint, so all three are valid topological orderings. Therefore, the answer 'All the above' is correct.