Problem $4$: Searching Directed Graphs $(12$ points$)$

Consider the following directed graph G:

a$)$ We perform Depth$-$First Search on G$.$ Which of these four orders of visiting the nodes is possible? Circle the answer, and draw the DFS tree that corresponds to it$.$ Use solid lines for discovery edges and dashed lines for back edges.

BCDGAFE

B ACDGFE

B ACFEDG

B ADCGFE

b$)$ Show the tree you would get if you performed Breadth$-$First Search on G$,$ starting with the same node. Use solid lines for discovery edges and dashed lines for cross edges.