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a 14 D 15 10- B Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit.

a 14 D 15 10- B Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit.

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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### Applying the Sorted Edges Algorithm #### Graph Explanation The image shows a weighted graph with four vertices labeled \(A\), \(B\), \(C\), and \(D\). The edges connecting these vertices have the following weights: - Edge \(A - C\): 1 - Edge \(A - D\): 5 - Edge \(A - B\): 10 - Edge \(C - D\): 14 - Edge \(C - B\): 6 - Edge \(D - B\): 15 #### Problem Statement **Task**: Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit. ### Steps Using the Sorted Edges Algorithm 1. **List the Edges in Order of Increasing Weight**: - \(A - C\): 1 - \(A - D\): 5 - \(C - B\): 6 - \(A - B\): 10 - \(C - D\): 14 - \(D - B\): 15 2. **Select Edges to Form a Circuit**: The sorted edges algorithm involves selecting edges in order of increasing weight, ensuring that no cycles are formed until all vertices are connected. - Select edge \(A - C\) (Weight 1) - Select edge \(A - D\) (Weight 5) - Select edge \(C - B\) (Weight 6) At this point, we have connected all vertices: \(A\), \(B\), \(C\), \(D\). Note that selecting the edge \(A - B\) would form a cycle. #### Total Cost Calculation The selected edges are: - \(A - C\) (Weight 1) - \(A - D\) (Weight 5) - \(C - B\) (Weight 6) **Total Cost** = 1 + 5 + 6 = 12 Therefore, the total cost of the resulting circuit is **12**.
Transcribed Image Text:### Applying the Sorted Edges Algorithm #### Graph Explanation The image shows a weighted graph with four vertices labeled \(A\), \(B\), \(C\), and \(D\). The edges connecting these vertices have the following weights: - Edge \(A - C\): 1 - Edge \(A - D\): 5 - Edge \(A - B\): 10 - Edge \(C - D\): 14 - Edge \(C - B\): 6 - Edge \(D - B\): 15 #### Problem Statement **Task**: Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit. ### Steps Using the Sorted Edges Algorithm 1. **List the Edges in Order of Increasing Weight**: - \(A - C\): 1 - \(A - D\): 5 - \(C - B\): 6 - \(A - B\): 10 - \(C - D\): 14 - \(D - B\): 15 2. **Select Edges to Form a Circuit**: The sorted edges algorithm involves selecting edges in order of increasing weight, ensuring that no cycles are formed until all vertices are connected. - Select edge \(A - C\) (Weight 1) - Select edge \(A - D\) (Weight 5) - Select edge \(C - B\) (Weight 6) At this point, we have connected all vertices: \(A\), \(B\), \(C\), \(D\). Note that selecting the edge \(A - B\) would form a cycle. #### Total Cost Calculation The selected edges are: - \(A - C\) (Weight 1) - \(A - D\) (Weight 5) - \(C - B\) (Weight 6) **Total Cost** = 1 + 5 + 6 = 12 Therefore, the total cost of the resulting circuit is **12**.
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