use kruskals algorithm to find the minimum spanning tree for the weighted graph. give the total weight of…

Explanation:

Step1: List all edges and weights

Edges and weights: $(A - B,10),(B - D,17),(D - E,19),(A - C,15),(C - E,32),(A - E,23),(B - C,27),(C - D,30)$

Step2: Sort edges by weight

Sorted: $(A - B,10),(A - C,15),(B - D,17),(D - E,19),(A - E,23),(B - C,27),(C - D,30),(C - E,32)$

Step3: Add edges to MST

Start adding edges in sorted - order without creating cycles. Add $(A - B)$ (weight = 10), $(A - C)$ (weight = 15), $(B - D)$ (weight = 17), $(D - E)$ (weight = 19)

Step4: Calculate total weight

Total weight = $10 + 15+17 + 19=61$

The minimum - spanning tree will have 4 edges connecting all 5 vertices without cycles. Analyzing the shape of the MST formed by the edges $(A - B),(A - C),(B - D),(D - E)$ helps in choosing the correct shape from the given options.

Answer:

The total weight of the minimum spanning tree is 61. (To determine the correct shape of the MST from the given options, one would need to visualize the connections made by the edges $(A - B),(A - C),(B - D),(D - E)$ among the vertices $A$, $B$, $C$, $D$, $E$.)