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Determine the total weight of the minimum Hamilton circuits?

Determine the total weight of the minimum Hamilton circuits?

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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Determine the total weight of the minimum Hamilton circuits? 
### Explanation of the Weighted Graph The image depicts a weighted graph consisting of four vertices labeled A, B, C, and D. The edges connecting these vertices are assigned specific weights as follows: - **Edge AD:** Weight 18 - **Edge AB:** Weight 10 - **Edge AC:** Weight 4 - **Edge BC:** Weight 23 - **Edge BD:** Weight 19 - **Edge CD:** Weight 29 - **Edge BD (Interior):** Weight 33 The vertices are connected as follows: - Vertex A is connected to Vertex D, Vertex B, and Vertex C. - Vertex B is connected to Vertex A, Vertex C, Vertex D (directly), and Vertex D through an interior edge. - Vertex C is connected to Vertex A, Vertex B, and Vertex D. - Vertex D is connected to Vertex A, Vertex B (directly), Vertex B through an interior edge, and Vertex C. ### Diagram Explanation: 1. **Vertices:** - A - B - C - D 2. **Edges and Weights:** - A to D (Weight = 18) - A to B (Weight = 10) - A to C (Weight = 4) - B to C (Weight = 23) - B to D (Weight = 19) - C to D (Weight = 29) - B to D (Interior, Weight = 33) ### Educational Context: This type of graph is useful in various applications such as networking, pathfinding, and optimization problems. Understanding weighted graphs helps in solving problems related to finding the shortest path, minimum spanning tree, and network flow. - **Use Case:** Prim's or Kruskal's algorithm can be used on this graph to find the minimum spanning tree, which is a subgraph that connects all vertices with the minimal total edge weight. - **Example Problem:** Determine the shortest path from Vertex A to Vertex D. - **Learning Outcome:** Students will be able to analyze and interpret weighted graphs, apply algorithms to find optimal paths, and understand network structure and optimization.
Transcribed Image Text:### Explanation of the Weighted Graph The image depicts a weighted graph consisting of four vertices labeled A, B, C, and D. The edges connecting these vertices are assigned specific weights as follows: - **Edge AD:** Weight 18 - **Edge AB:** Weight 10 - **Edge AC:** Weight 4 - **Edge BC:** Weight 23 - **Edge BD:** Weight 19 - **Edge CD:** Weight 29 - **Edge BD (Interior):** Weight 33 The vertices are connected as follows: - Vertex A is connected to Vertex D, Vertex B, and Vertex C. - Vertex B is connected to Vertex A, Vertex C, Vertex D (directly), and Vertex D through an interior edge. - Vertex C is connected to Vertex A, Vertex B, and Vertex D. - Vertex D is connected to Vertex A, Vertex B (directly), Vertex B through an interior edge, and Vertex C. ### Diagram Explanation: 1. **Vertices:** - A - B - C - D 2. **Edges and Weights:** - A to D (Weight = 18) - A to B (Weight = 10) - A to C (Weight = 4) - B to C (Weight = 23) - B to D (Weight = 19) - C to D (Weight = 29) - B to D (Interior, Weight = 33) ### Educational Context: This type of graph is useful in various applications such as networking, pathfinding, and optimization problems. Understanding weighted graphs helps in solving problems related to finding the shortest path, minimum spanning tree, and network flow. - **Use Case:** Prim's or Kruskal's algorithm can be used on this graph to find the minimum spanning tree, which is a subgraph that connects all vertices with the minimal total edge weight. - **Example Problem:** Determine the shortest path from Vertex A to Vertex D. - **Learning Outcome:** Students will be able to analyze and interpret weighted graphs, apply algorithms to find optimal paths, and understand network structure and optimization.
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