$6.$ Consider the graph

$($a$)(12\mathrm{.}3,\backslash$#$1($c$))$ Use Kruskal's algorithm to find a spanning tree of minimum total weight. Give the weight of your minimum tree and show your steps.

$($b$)(12\mathrm{.}3,\backslash$#$2($c$))$ Apply Prim's algorithm to find a minimum spanning tree different from the one in part $($a$).$ Start at vertex $\backslash ($ E $\backslash ),$ explain your reasoning, and draw the tree.