$(25$ points$)$ Answer the questions using the following graph.

$($a$)$ List the node sequences of DFS and BFS starting from F$.($Follow the order of the node label whenever a choice is needed.$)$

$($b$)$ Draw the sequence of edges $($represented by edge weight$)$ added to the minimal$-$cost spanning tree by the Kruskal's algorithm.

$($c$)$ Do the same thing as $($b$)$ using Prim's algorithm.

$($d$)$ Do the same thing as $($b$)$ using Sollin's algorithm.

$($e$)$ Find the shortest paths from $F$ to all other vertices using Dijkstra's algorithm.