Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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A sales Director who lives in a city a is required to fly to a regional‘s office and cities BCD in E. The weather graph shows the one-way airfares between any two cities. Use the brunt force method to find the optimal solution. 
**Graph Representation and Explanation:**

The image provides a weighted undirected graph in the shape of a pentagon with an internal star. The vertices of the graph are labeled A, B, C, D, and E. The edges connecting these vertices are labeled with weights.

- **Vertices and Edges:**
  - Vertex A is connected to:
    - B with a weight of 204
    - C with a weight of 363
    - D with a weight of 136
    - E with a weight of 109
  - Vertex B is connected to:
    - C with a weight of 168
    - D with a weight of 199
    - E with a weight of 441
  - Vertex C is connected to:
    - D with a weight of 139
    - E with a weight of 286
  - Vertex D is connected to:
    - E with a weight of 419

The edges form a pentagon with a star inside, indicating that every vertex is directly connected to every other vertex. Consequently, this is a representation of a complete graph, specifically \( K_5 \).

- **Edge Weights:**
  - A - B: 204
  - A - C: 363
  - A - D: 136
  - A - E: 109
  - B - C: 168
  - B - D: 199
  - B - E: 441
  - C - D: 139
  - C - E: 286
  - D - E: 419

This type of graph can be used to model various scenarios where multiple points need to be interconnected, each with a certain cost or distance, such as network design, travel planning, and more. The structure highlights the complexity and various paths one can take to traverse between any two points.
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Transcribed Image Text:**Graph Representation and Explanation:** The image provides a weighted undirected graph in the shape of a pentagon with an internal star. The vertices of the graph are labeled A, B, C, D, and E. The edges connecting these vertices are labeled with weights. - **Vertices and Edges:** - Vertex A is connected to: - B with a weight of 204 - C with a weight of 363 - D with a weight of 136 - E with a weight of 109 - Vertex B is connected to: - C with a weight of 168 - D with a weight of 199 - E with a weight of 441 - Vertex C is connected to: - D with a weight of 139 - E with a weight of 286 - Vertex D is connected to: - E with a weight of 419 The edges form a pentagon with a star inside, indicating that every vertex is directly connected to every other vertex. Consequently, this is a representation of a complete graph, specifically \( K_5 \). - **Edge Weights:** - A - B: 204 - A - C: 363 - A - D: 136 - A - E: 109 - B - C: 168 - B - D: 199 - B - E: 441 - C - D: 139 - C - E: 286 - D - E: 419 This type of graph can be used to model various scenarios where multiple points need to be interconnected, each with a certain cost or distance, such as network design, travel planning, and more. The structure highlights the complexity and various paths one can take to traverse between any two points.
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