use kruskals algorithm to find the minimum spanning tree for the weighted graph. give the total weight of…
use kruskals algorithm to find the minimum spanning tree for the weighted graph. give the total weight of the minimum spanning tree. which of the following trees matches the shape of the minimum spanning tree? what is the total weight of the minimum spanning tree? the total weight is . (type an integer or a decimal.)
Answer
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: Select edges for 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 = $10 + 15+17 + 19=61$.
Answer:
The shape of the minimum - spanning tree is the one that has 4 edges connecting 5 vertices in a non - cyclic way. The total weight is 61.