$(6$ points$)$ Consider the following weighted undirected graph.

$($a$)(2$ points$)$ Explain why edge $(B,E)$ is safe. In other words, give a cut where the edge is the cheapest edge crossing the cut.

$($b$)(2$ points$)$ Suppose we run the Kruskal's algorithm on this graph. List the edges appearing in the Minimum Spanning Tree $($MST$)$ in the order they are added to the MST$.$ If you prefer, you are allowed to index edges by their weight. $($e$.$g$.$ Instead of DF$,$ GH$,...,$ you can write $1,2,$dots,

$($c$)(2$ points$)$ Suppose we run the Prim's algorithm on this graph using A as initial vertex. List the edges appearing in the Minimum Spanning Tree $($MST$)$ in the order they are added to the MST$.$