$(10$ points$)$ In this problem, you will show the execution of the minimum spanning tree algorithms that

you studied in class on the following graph:

$($a$)$ Trace the execution of Prim's algorithm to find the minimum spanning tree for this graph. At each

step, you should show the vertex and the edge added to the tree and the resulting values of D after

the relaxation operation. Use START vertex as the first vertex in your traversal.

$($b$)$ Trace the execution of Kruskal's algorithm to find the minimum spanning tree for this graph. Give

a list of edges in the order in which thy are added to the MST$.$