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43 D 3 40 39- 10. 201 B 15 E 31 37 A Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. What is the total cost of the tree?

43 D 3 40 39- 10. 201 B 15 E 31 37 A Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. What is the total cost of the tree?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 15E
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**Minimum Cost Spanning Tree using Kruskal’s Algorithm** **Graph Description:** The graph consists of five vertices labeled as A, B, C, D, and E. The edges between these vertices are labeled with their respective weights as follows: - A to B: 31 - A to C: 40 - A to D: 20 - A to E: 15 - B to C: 33 - B to D: 4 - B to E: 10 - C to D: 43 - C to E: 37 - D to E: 39 **Problem Statement:** Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. What is the total cost of the tree? **Solution:** 1. **List all edges in ascending order based on their weights:** - B to D: 4 - B to E: 10 - A to E: 15 - A to D: 20 - A to B: 31 - B to C: 33 - A to C: 40 - D to E: 39 - A to C: 40 - C to D: 43 2. **Select the smallest weight edge that does not form a cycle:** - B to D: 4 - B to E: 10 - A to E: 15 - A to D: 20 3. **Total minimum cost calculation:** - Total cost = 4 (B to D) + 10 (B to E) + 15 (A to E) + 20 (A to D) - Total cost = 49 The minimum cost spanning tree using Kruskal's algorithm has a total cost of **49**.
Transcribed Image Text:**Minimum Cost Spanning Tree using Kruskal’s Algorithm** **Graph Description:** The graph consists of five vertices labeled as A, B, C, D, and E. The edges between these vertices are labeled with their respective weights as follows: - A to B: 31 - A to C: 40 - A to D: 20 - A to E: 15 - B to C: 33 - B to D: 4 - B to E: 10 - C to D: 43 - C to E: 37 - D to E: 39 **Problem Statement:** Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. What is the total cost of the tree? **Solution:** 1. **List all edges in ascending order based on their weights:** - B to D: 4 - B to E: 10 - A to E: 15 - A to D: 20 - A to B: 31 - B to C: 33 - A to C: 40 - D to E: 39 - A to C: 40 - C to D: 43 2. **Select the smallest weight edge that does not form a cycle:** - B to D: 4 - B to E: 10 - A to E: 15 - A to D: 20 3. **Total minimum cost calculation:** - Total cost = 4 (B to D) + 10 (B to E) + 15 (A to E) + 20 (A to D) - Total cost = 49 The minimum cost spanning tree using Kruskal's algorithm has a total cost of **49**.
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