hamilton path & topological sort

Question

I'm trying to prove that a Hamilton path is the only topological sort. I think I need to show that in case there are two topological sorts, none of them is a Hamilton path.

How can I prove that a Hamilton path is the only topological sort in a DAG?

Answer 1

The main thing you need to observe is that an Hamilton path is a path that goes through all vertices. Think how can one dag have 2 different topological sorts