A 42 34 30 35 12 B. 20

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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### Problem Statement

2. Determine the circuit of minimal length in the given graph.

### Graph Description

The graph is composed of four nodes labeled A, B, C, and D, forming a quadrilateral with diagonals:

- **Edges and Weights:**
  - A to B: 20
  - A to C: 42
  - A to D: 30
  - B to C: 35
  - B to D: 34
  - C to D: 12

### Explanation

This graph is a complete graph with each node connected to every other node. To determine the circuit of minimal length, consider the sum of the weights on the edges, ensuring each node is visited exactly once before returning to the start. The goal is to find the path that results in the smallest possible sum of weights.

**Steps to Find Minimal Circuit:**
1. List all possible circuits.
2. Calculate the total weight for each circuit.
3. Identify the circuit with the smallest total weight.

Consider using algorithms like the nearest neighbor or others used for solving the Traveling Salesman Problem to find the optimal path efficiently.

This task promotes understanding of graph theory, specifically concepts related to circuits and minimal paths in weighted graphs.
Transcribed Image Text:### Problem Statement 2. Determine the circuit of minimal length in the given graph. ### Graph Description The graph is composed of four nodes labeled A, B, C, and D, forming a quadrilateral with diagonals: - **Edges and Weights:** - A to B: 20 - A to C: 42 - A to D: 30 - B to C: 35 - B to D: 34 - C to D: 12 ### Explanation This graph is a complete graph with each node connected to every other node. To determine the circuit of minimal length, consider the sum of the weights on the edges, ensuring each node is visited exactly once before returning to the start. The goal is to find the path that results in the smallest possible sum of weights. **Steps to Find Minimal Circuit:** 1. List all possible circuits. 2. Calculate the total weight for each circuit. 3. Identify the circuit with the smallest total weight. Consider using algorithms like the nearest neighbor or others used for solving the Traveling Salesman Problem to find the optimal path efficiently. This task promotes understanding of graph theory, specifically concepts related to circuits and minimal paths in weighted graphs.
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