$1.(6$ points$)$ Consider the following digraph. Assume the vertex adjacency lists are in sorted order: For example, when iterating through the edges pointing from $\backslash ($ t $\backslash ),$ consider the edge $\backslash ($ t $\backslash )\backslash (\backslash$rightarrow x $\backslash )$ before $\backslash ($ t $\backslash$rightarrow y $\backslash ).$

a$.$ Run depth$-$first search on the digraph, starting from vertex $\backslash (\backslash$boldsymbol$\{$q$\}\backslash ).$ List the vertices in postorder.

Vertices:

b$.$ Run breadth$-$first search on the digraph, starting from vertex $\backslash (\backslash$boldsymbol$\{$q$\}\backslash ).$ List the vertices in the order in which they are de$-$queued from the FIFO queue.