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2) Consider the following weighted graph: F 8. 9 15 8 12 A E 61 2 G 13 7 10 11 4 17 3 B D 5 2 с Use Kruskal's Algorithm to determine the minimum cost spanning tree for this graph. Then, please draw the tree and give its cost.

2) Consider the following weighted graph: F 8. 9 15 8 12 A E 61 2 G 13 7 10 11 4 17 3 B D 5 2 с Use Kruskal's Algorithm to determine the minimum cost spanning tree for this graph. Then, please draw the tree and give its cost.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Problem 2: Weighted Graph Analysis **Task:** Consider the following weighted graph. **Graph Details:** - **Vertices:** There are six vertices in the graph, labeled A, B, C, D, E, and F. - **Edges and Weights:** - A to B: 7 - A to C: 6 - A to D: 8 - A to E: 9 - A to F: 8 - B to C: 2 - B to D: 1 - B to E: 3 - B to F: 7 - C to D: 1 - C to E: 5 - C to F: 15 - D to E: 10 - D to F: 12 - E to F: 2 - G to A: 15 - G to B: 4 - G to C: 5 - G to D: 17 - G to E: 13 - G to F: 8 **Instructions:** Use **Kruskal's Algorithm** to determine the minimum cost spanning tree for this graph. Then, draw the tree and provide its cost. **Explaining Kruskal’s Algorithm:** 1. **Sort** all the edges in non-decreasing order of their weight. 2. **Initialize** the minimum spanning tree with no edges. 3. **Add edges** to the minimum spanning tree, one by one, using the sorted list, making sure no cycles are formed. 4. Stop when there are exactly \( V-1 \) edges in the tree, where \( V \) is the number of vertices in the graph. **Purpose:** This exercise will help in understanding how Kruskal’s algorithm can be applied for finding a minimum spanning tree in a graph, which is useful in network design, such as designing least cost networks.
Transcribed Image Text:### Problem 2: Weighted Graph Analysis **Task:** Consider the following weighted graph. **Graph Details:** - **Vertices:** There are six vertices in the graph, labeled A, B, C, D, E, and F. - **Edges and Weights:** - A to B: 7 - A to C: 6 - A to D: 8 - A to E: 9 - A to F: 8 - B to C: 2 - B to D: 1 - B to E: 3 - B to F: 7 - C to D: 1 - C to E: 5 - C to F: 15 - D to E: 10 - D to F: 12 - E to F: 2 - G to A: 15 - G to B: 4 - G to C: 5 - G to D: 17 - G to E: 13 - G to F: 8 **Instructions:** Use **Kruskal's Algorithm** to determine the minimum cost spanning tree for this graph. Then, draw the tree and provide its cost. **Explaining Kruskal’s Algorithm:** 1. **Sort** all the edges in non-decreasing order of their weight. 2. **Initialize** the minimum spanning tree with no edges. 3. **Add edges** to the minimum spanning tree, one by one, using the sorted list, making sure no cycles are formed. 4. Stop when there are exactly \( V-1 \) edges in the tree, where \( V \) is the number of vertices in the graph. **Purpose:** This exercise will help in understanding how Kruskal’s algorithm can be applied for finding a minimum spanning tree in a graph, which is useful in network design, such as designing least cost networks.
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