Q$3.(40$ points$)$

Consider the following directed graph:

a$.$ Construct a depth$-$first search tree starting at node $g.$ Break all ties by picking the vertex that comes, alphabetically: Show your work $($include the order in which vertices are discovered, the order in which versices? are processed, numbering the edges, plus any forward, back and cross edges in the DFS tree$).$

b$.$ Construct a breadth$-$first search tree starting at node $g.$ Break all ties by picking the vertex that comes first alphabetically. Show your work $($include the order in which vertices are discovered, the order in which vertices $.$ are processed, numbering the edges, plus any forward, back and cross edges in the BFS tree$).$