$***$ Consider the complete graph $K_n$ with labeled vertices $1,2,$cdots,$n$ in which each edge joining vertices i and $j$ is weighted $c((i,j))=i+j$ for all $ij.$

$($a$)$ Apply Prim's algorithm starting at vertex $2$ in $K_4$ to determine a minimum weight spanning tree for $K_4.$

$($b$)$ Apply Kruskal's greedy algorithm to determine a minimum weight spanning tree for $K_4.$ Is what you found the same as your answer to part $(a)?$

$($c$)$ Apply either Kruskal's greedy algorithm or Prim's algorithm to determine a minimum weight spanning tree for $K_n,n2.$