11 D 10 A 15 B Apply the sorted edges algorithm to the graph above. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDA
11 D 10 A 15 B Apply the sorted edges algorithm to the graph above. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDA
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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Transcribed Image Text:### Problem Description
**Graph and Algorithm Application**
Consider the graph displayed above. The graph consists of four vertices labeled as A, B, C, and D, and six edges connecting these vertices.
#### Edge Details:
- Edge connecting vertex C to vertex A with a weight of 4.
- Edge connecting vertex C to vertex B with a weight of 3.
- Edge connecting vertex A to vertex B with a weight of 15.
- Edge connecting vertex D to vertex A with a weight of 10.
- Edge connecting vertex D to vertex B with a weight of 5.
- Edge connecting vertex D to vertex C with a weight of 11.
#### Task:
Apply the sorted edges algorithm to the graph above. Provide your answer as a list of vertices, starting and ending at vertex A.
**Example:** If the resulting path is ABCDA, simply write: ABCDA.
---
**Instructions:**
To apply the sorted edges algorithm, follow these steps:
1. **List All Edges and Their Weights:**
- CA: 4
- CB: 3
- AB: 15
- DA: 10
- DB: 5
- DC: 11
2. **Sort the Edges by Increasing Order of Weights:**
- CB: 3
- CA: 4
- DB: 5
- DA: 10
- DC: 11
- AB: 15
3. **Construct the Path:**
- Start from vertex A.
- Choose edges in the sorted order to form the path.
Provide the final sequence of vertices based on the sorted edges algorithm.
**Note:** For educational purposes, ensure you explain each step clearly and verify if the resulting path forms a simple cycle that visits every vertex exactly once before returning to the starting vertex A.
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