We say that a digraph G has "property X$",$ if there is an order of the vertices, such that when running DFS on G with that order of vertices for the choices in the main loop, the resulting directed spanning forest has no arcs in it $($at all$).$

Which of the following statements is true?

If G has property X$,$ then G is not connected.

It is not possible to characterise such G$.$

G has property X iff G is a dag.

Only small G may have property X$.$

If G is a dag, then G has not property X$.$

Such digraphs do not exist.