Questions: Use Kruskal's algorithm to find a minimum spanning tree for the graph. Find the total weight of this minimum spanning tree. Find a minimum spanning tree. Choose the correct answer below. A. B. C. D. The total weight for this minimum spanning tree is (Type a whole number.)

Use Kruskal's algorithm to find a minimum spanning tree for the graph. Find the total weight of this minimum spanning tree.

Find a minimum spanning tree. Choose the correct answer below.
A. B.
C. D.

The total weight for this minimum spanning tree is
(Type a whole number.)

Transcript text: Use Kruskal's algorithm to find a minimum spanning tree for the graph. Find the total weight of this minimum spanning tree. Find a minimum spanning tree. Choose the correct answer below. A. B. C. D. The total weight for this minimum spanning tree is $\square$ (Type a whole number.)

Solution

Solution Steps

Step 1: List all edges in ascending order of weight

Edge AG: weight 2
Edge AB: weight 3
Edge BC: weight 6
Edge AC: weight 9
Edge CF: weight 13
Edge CD: weight 14
Edge DE: weight 17
Edge GF: weight 20
Edge BE: weight 20

Step 2: Select the smallest edge and add it to the MST

Add edge AG (weight 2)

Step 3: Select the next smallest edge that doesn't form a cycle

Add edge AB (weight 3)

Step 4: Continue selecting the smallest edge that doesn't form a cycle

Add edge BC (weight 6)
Add edge AC (weight 9)
Add edge CF (weight 13)
Add edge DE (weight 17)

Step 5: Verify the MST and calculate the total weight

The edges in the MST are AG, AB, BC, AC, CF, and DE.
Total weight = 2 + 3 + 6 + 9 + 13 + 17 = 50

Final Answer

The total weight for this minimum spanning tree is 50. The correct answer is option C.

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