We can start either from vertex 4 or from vertex 6 because only these 2 have no incoming edge.
Therefore option B , D will be considered
Starting from vertex 4, next vertex can be 5 or 6.(order: 4)
considering vertex 5, next vertex can be 2 or 6 (order: 4,5) | considering vertex 6, next vertex can be 5.(order:4,6)
considering vertex 6, next vertex can be 2(order: 4,5,6) | considering vertex 5, next vertex will be 2.(order:4,6,5)
or | considering vertex 2, next vertex can be 1,3(order:4,6,5,2)
considering vertex 2,next vertex can be 6(order:4,5,2) | finally correct order can be (4,6,5,2,3,1) or (4,6,5,2,1,3)
considering order 4,5,6 next vertex 2: order(4,5,6,2) | no option
considering order 4,5,2, next vertex 6 : order (4,5,2,6) |
considering order(4,5,6,2)or(4,5,2,6) ,next vertex can be 1,3 |
finally correct order can be (4,5,6,2,1,3) or (4,5,6,2,3,1) or (4,5,2,6,1,3),(4,5,2,6,3,1)----------no option
therefore option B is wrong
Starting from vertex 6, next vertex will be 4.(order: 6)
considering vertex 4, next vertex will be 5.(order: 6,4)
considering vertex 5, next vertex will be 2.(order: 6,4,5)
considering vertex 2, next vertex can be 1,3.(order: 6,4,5,2)
finally correct order can be (6,4,5,2,1,3) or (6,4,5,2,3,1)
The correct ans is option D. (6, 4, 5, 2, 1, 3)