Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
See similar textbooks
icon
Related questions
Question
### 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.
Expert Solution
Step 1

Please find the attachment

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS