Consider the following graph with the numbers representing the weight of each edge: $[2]$

a

b

c

d

e

f

g

h

$10$

$1$

$4$

$3$

$2$

$0$

$8$

$2$

$7$

$1$

$6$

$8$

$9$

$12$

Find the weight of the minimal spanning tree of this graph.

A$.15$ B$.17$ C$.20$ D$.24$ E$.25$

$21.$ For the graph in Question $20,$ what is the minimum number of edges that need to be $[2]$

removed to make the graph a tree?

A$.4$ B$.5$ C$.6$ D$.7$ E$.8$

$22.$ For the graph in Question $20,$ which of the following statements about its minimal $[2]$

spanning trees $($MSTs$)$ is CORRECT?

A$.$ An MST created by Kruskal$$s algorithm can have total weight greater than an

MST created by Prim$$s algorithm

B$.$ An MST created by Prim$$s algorithm can have total weight greater than an

MST created by Kruskal$$s algorithm

C$.$ Any MST created by Kruskal$$s algorithm and any MST created by Prim$$s

algorithm will include the edge $($a$,$ c$).$

D$.$ Both Kruskal$$s and Prim$$s algorithm require that the first two edges chosen

are $($b$,$ e$)$ followed by $($e$,$ f$).$

E$.$ Both Kruskal$$s and Prim$$s algorithm require the edge $($g$,$ h$)$ to be included