$(10$ points$)$ Consider the graph $G$ depicted below, and perform the following graph search algorithms.

Whenever faced with a decision of which vertex to pick from a set of vertices, pick the vertex whose

label occurs earliest in the alphabet.

$($a$)$ Trace the execution of BFS beginning at vertex $A,$ labeling each edge as a discovery or cross edge.

$($b$)$ Trace the execution of DFS beginning at vertex $A,$ labeling each edge as a discovery or back edge.