Question $2$: Consider the following directed graph:

$(2\mathrm{.}1)$ Draw the $DFS-$forest obtained by running algorithm DFS$.$ Classify each edge as a tree edge, forward edge, back edge, or cross edge. In the DFS$-$forest, give the pre$-$ and post$-$number of each vertex. Whenever there is a choice of vertices, pick the one that is alphabetically first.

$(2\mathrm{.}2)$ Draw the $DFS-$forest obtained by running algorithm DFS$.$ Classify each edge as a tree edge, forward edge, back edge, or cross edge. In the DFS$-$forest, give the pre$-$ and post$-$number of each vertex. Whenever there is a choice of vertices, pick the one that is alphabetically last.

Note that in $(2\mathrm{.}1)$ algorithm DFS$($G$)$ starts by calling Explore$($A$),$ Explore for vertex A$.$

Note that in $(2\mathrm{.}2)$ algorithm DFS$($G$)$ starts by calling Explore$($G$),$ Explore for vertex $G.$