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15 D 8 2 B E 14 10 A Apply the sorted edges algorithm to the graph above. Find the total cost of the resulting circuit.

15 D 8 2 B E 14 10 A 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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## Graph Theory: Sorted Edges Algorithm ### Understanding the Graph The image shows a weighted graph with five vertices labeled **A**, **B**, **C**, **D**, and **E**. The weights of the edges are indicated as numbers between the vertices. ### Graph Representation - Vertices: **A**, **B**, **C**, **D**, **E** - Edges with Weights: - Between **C** and **B**: 11 - Between **B** and **A**: 14 - Between **A** and **E**: 10 - Between **E** and **D**: 6 - Between **D** and **C**: 15 - Between **D** and **A**: 7 - Between **C** and **A**: 1 - Between **B** and **D**: 8 - Between **B** and **A** (second edge): 5 - Between **A** and **B** (third edge): 2 ### Sorted Edges Algorithm The sorted edges algorithm, also known as Kruskal’s algorithm, is a method for finding the minimum spanning tree (MST) of a connected weighted graph. It operates by: 1. Sorting all edges in the graph by their weights in ascending order. 2. Adding the shortest edge to the MST, ensuring no cycles are formed, until all vertices are connected, forming the MST. ### Applying the Sorted Edges Algorithm To apply the sorted edges algorithm to the graph above, follow these steps: 1. **List all edges and sort by weight**: - (C, A): 1 - (A, B): 2 - (B, A): 5 - (E, D): 6 - (D, A): 7 - (B, D): 8 - (A, E): 10 - (C, B): 11 - (B, A): 14 - (D, C): 15 2. **Select edges for MST** ensuring no cycles: - Add (C, A) - weight 1 - Add (A, B) - weight 2 - Add (E, D) - weight 6
Transcribed Image Text:## Graph Theory: Sorted Edges Algorithm ### Understanding the Graph The image shows a weighted graph with five vertices labeled **A**, **B**, **C**, **D**, and **E**. The weights of the edges are indicated as numbers between the vertices. ### Graph Representation - Vertices: **A**, **B**, **C**, **D**, **E** - Edges with Weights: - Between **C** and **B**: 11 - Between **B** and **A**: 14 - Between **A** and **E**: 10 - Between **E** and **D**: 6 - Between **D** and **C**: 15 - Between **D** and **A**: 7 - Between **C** and **A**: 1 - Between **B** and **D**: 8 - Between **B** and **A** (second edge): 5 - Between **A** and **B** (third edge): 2 ### Sorted Edges Algorithm The sorted edges algorithm, also known as Kruskal’s algorithm, is a method for finding the minimum spanning tree (MST) of a connected weighted graph. It operates by: 1. Sorting all edges in the graph by their weights in ascending order. 2. Adding the shortest edge to the MST, ensuring no cycles are formed, until all vertices are connected, forming the MST. ### Applying the Sorted Edges Algorithm To apply the sorted edges algorithm to the graph above, follow these steps: 1. **List all edges and sort by weight**: - (C, A): 1 - (A, B): 2 - (B, A): 5 - (E, D): 6 - (D, A): 7 - (B, D): 8 - (A, E): 10 - (C, B): 11 - (B, A): 14 - (D, C): 15 2. **Select edges for MST** ensuring no cycles: - Add (C, A) - weight 1 - Add (A, B) - weight 2 - Add (E, D) - weight 6
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