Question $2$: Practice with DFS and BFS $(10$ points$)$

None of the questions below need explanations. They are all full$-$credit or no$-$credit.

a$.$ List the sequence of vertices visited by depth$-$first search, starting at the point A $.$ When multiple vertices can be chosen to be visited at a given time, settle the tie by visiting the vertex that comes first alphabetically. Each vertex should be visited only once. An example $($incorrect$)$ answer should look like: $($A$,$ B$,$ F$,$ E$,...,$ J$,$ K$)(3$ points$)$

b$.$ List the sequence of vertices visited by a breadth$-$first search, starting at the point A $.$ When multiple vertices can be chosen to be visited at a given time, settle the tie by visiting the vertex that comes first alphabetically. Each vertex should be visited only once. $(3$ points$)$

c$.$ Breadth$-$first search starting at A would mark A as depth $0.$ Any adjacent vertices will be marked with depth $1.$ The next wave would have depth $2,$ then $3,$ and so on$.$ Redraw the graph above and mark each vertex with the depth from breadth$-$first search starting at A$.(2$ points$)$

d$.$ What is the greatest possible depth of a vertex in the above graph if you are able to start breadth$-$first search from any point on the graph? $(2$ points$)$