Topological search and Breadth first search
algorithm, graph
Solution
A mere BFS is only sufficient for a tree (or forest of trees), because in (forest of) trees, in-degrees are at most 1. Now, look at this case:
B → C → D
↗
A
A BFS where queue is initialized to `A B` (whose in-degrees are zero) will return `A B D C`, which is not topologically sorted. That's why you have to maintain in-degrees count, and only pick nodes whose count has dropped to zero. (*)
BTW, this is the flaw of your 'reason' : BFS only guarantee one parent has been visited before, not all of them.
Edit: (*) In other words you push back adjacent nodes whose in-degree is zero (in the exemple, after processing `A`, `D` would be skipped). So, you're still using a queue and you've just added a filtering step to the general algorithm. That being said, continuing to call it a BFS is questionable.
Problem
Is it possible to use Breadth first search logic to do a topological sort of a DAG? The solution in Cormen makes use of Depth first search but wouldn't be easier to use BFS? Reason: BFS visits all the nodes in a particular depth before visiting nodes with the next depth value. It naturally means that the parents will be listed before the children if we do a BFS. Isn't this exactly what we need for a topological sort?