For problems $2),3),$ and $4),$ refer to the following graph:

$(10$ points$)$ Ignore the directions of the edges, execute Kruskal's algorithm to find an MST$.$ List the edges selected by the algorithm in the order of their selection, assuming that edges of equal weights are considered for selection in alphabetical order. Note: in an undirected graph, each edge is denoted $(,)$ with $$ preceding $$ alphabetically, e$.$g$.,$ the edge with cost $3$ in the undirected graph is denoted $($C$,$F$)$ rather than $($F$,$C$).$

$(10$ points$)$ Show the results of executing a DFS on the directed graph, starting from vertex A and fill out the table below. Assume that the next eligible vertex to visit is selected in alphabetical order.

$\backslash$table$[[,$A$,$B$,$C$,$D$,$E$,$F$],[$discover time $ud,1,,,,,],[$finish time $uf,,,,,,]]$

$(15$ points$)$ Ignore the edge weights and assume all edge costs are unity or one, use Warshall's algorithm to determine the number of different paths of length $2$ from vertex $F$ to each of $A,B,C,D,E,F.$