Problem$4.$ Given the following graph

a$.$ Show the minimum$-$cost$-$spanning$-$tree $($MST$)$ rooted at vertex $1$ as produced by Kruskal $\text{'}$s algorithm. Show the result after each iteration, and the final MST$.$

b$.$ Show the minimum$-$cost$-$spanning$-$tree $($MST$)$ rooted at vertex $1$ as produced by PRIM's algorithm. Show the result after each iteration, and the final MST$.$

c$.$ Use Dijkstra's algorithm, with vertex $1$ as the source, to find the single$-$source$-$shortest$-$paths spanning tree. Show the result after each iteration, and the final tree.