Questions: Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. Which of the edges below are included in the minimum cost tree? AC AE AB BC CD CE DE AD BD BE

Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. Which of the edges below are included in the minimum cost tree? AC AE AB BC CD CE DE AD BD BE
Transcript text: Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. Which of the edges below are included in the minimum cost tree? AC AE $A B$ $B C$ $C D$ CE DE AD $B D$ BE
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Solution

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Solution Steps

Step 1: List All Edges with Their Weights

List all the edges in the graph along with their weights:

  • AB: 2
  • AC: 8
  • AD: 9
  • AE: 6
  • BC: 15
  • BD: 12
  • BE: 14
  • CD: 5
  • CE: 11
  • DE: 4
Step 2: Sort Edges by Weight

Sort the edges in ascending order of their weights:

  1. AB: 2
  2. DE: 4
  3. CD: 5
  4. AE: 6
  5. AC: 8
  6. AD: 9
  7. CE: 11
  8. BD: 12
  9. BE: 14
  10. BC: 15
Step 3: Apply Kruskal's Algorithm

Start adding edges to the Minimum Spanning Tree (MST) from the sorted list, ensuring no cycles are formed:

  1. Add AB (2)
  2. Add DE (4)
  3. Add CD (5)
  4. Add AE (6)
  5. Add AC (8)

Final Answer

The edges included in the minimum cost spanning tree are:

  • AB
  • DE
  • CD
  • AE
  • AC
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