Let G$=($V$,$E$)$ be the following weighted graph:

V$=\{1,2,3,4,5,6,7,8,9,10,11,12\}$

E$=\{[(1,12)6],[(1,8)5],[(2,8)2],[(12,8)2],[(12,10)2],[(6,12)3],[(6,8)2],[(8,10)4],$

$[(10,6)5],[(10,4)3],[(10,3)5],[(3,4)3],[(4,11)2],[(4,5)7],[(11,5)1],[(3,9)2],[(2,9)8],$

$[(2,7)1]\},[(9,7)2]\},$ where $[($i$,$j$)$ a$]$ means that $($i$,$j$)$ is an edge of weight a$.$

a$.$ Use the greedy method $($Kruskal$$s algorithm$)$ to find a minimum spanning tree of G$.$ Show

the tree after every step of the algorithm.

b$.$ Using the greedy Dijkstra$$s single$-$source shortest$-$path algorithm, find the distances between

node $1$ and all the other nodes. Show the values of the DIST array at every step.

c$.$ Show the actual shortest paths of part $($b$).$ Note that these paths together form a spanning tree

of G$.$ Is this tree a minimum spanning tree?

Can you give me the solution with the tree diagrams at each step