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.)
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Solution

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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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