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A 5 2 9 4 6 B 2 8 5 7 D 3 C

A 5 2 9 4 6 B 2 8 5 7 D 3 C

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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Use the graph and find the nearest neighbor algorithm to find a Hamilton circuit that begins at vertex B.
### Understanding Graphs: Weighted Graph Example Welcome to our educational page dedicated to understanding graphs, specifically weighted graphs. In this example, we will explore the structure and components of a weighted graph, which is commonly used in fields such as computer science, networking, and transportation planning. #### Image Description The image above displays a weighted graph. A weighted graph is a type of mathematical graph in which each edge (connection between two vertices, or points) has a numerical value (weight) associated with it. These weights can represent various things, such as distances, costs, or times. #### Key Components of the Weighted Graph: - **Vertices (Nodes):** Points where edges meet. In this graph, the vertices are labeled as A, B, C, D, and E. - **Edges (Connections):** The connections between vertices. Each edge is represented by a line connecting two vertices. - **Weights:** Numerical values assigned to the edges. These values are usually written along the edges. In this graph, the weights range from 2 to 9. #### Detailed Explanation of the Graph: 1. **Vertices:** - A, B, C, D, and E are the vertices of the graph. 2. **Edges and Weights:** - Edge AB has a weight of 2. - Edge AC has a weight of 4. - Edge AD has a weight of 8. - Edge AE has a weight of 5. - Edge BC has a weight of 7. - Edge BD has a weight of 5. - Edge BE has a weight of 6. - Edge CD has a weight of 3. - Edge CE has a weight of 2. - Edge DE has a weight of 9. #### Applications: Weighted graphs are used in various applications: - **Network Design:** Optimizing paths for minimal cost or maximum efficiency. - **Transportation:** Planning routes and understanding the shortest or safest paths. - **Project Management:** Determining critical paths in task schedules. Understanding weighted graphs is crucial for solving real-world problems that require efficient decision-making based on multiple factors. This example helps illustrate the basic components and usage of weighted graphs.
Transcribed Image Text:### Understanding Graphs: Weighted Graph Example Welcome to our educational page dedicated to understanding graphs, specifically weighted graphs. In this example, we will explore the structure and components of a weighted graph, which is commonly used in fields such as computer science, networking, and transportation planning. #### Image Description The image above displays a weighted graph. A weighted graph is a type of mathematical graph in which each edge (connection between two vertices, or points) has a numerical value (weight) associated with it. These weights can represent various things, such as distances, costs, or times. #### Key Components of the Weighted Graph: - **Vertices (Nodes):** Points where edges meet. In this graph, the vertices are labeled as A, B, C, D, and E. - **Edges (Connections):** The connections between vertices. Each edge is represented by a line connecting two vertices. - **Weights:** Numerical values assigned to the edges. These values are usually written along the edges. In this graph, the weights range from 2 to 9. #### Detailed Explanation of the Graph: 1. **Vertices:** - A, B, C, D, and E are the vertices of the graph. 2. **Edges and Weights:** - Edge AB has a weight of 2. - Edge AC has a weight of 4. - Edge AD has a weight of 8. - Edge AE has a weight of 5. - Edge BC has a weight of 7. - Edge BD has a weight of 5. - Edge BE has a weight of 6. - Edge CD has a weight of 3. - Edge CE has a weight of 2. - Edge DE has a weight of 9. #### Applications: Weighted graphs are used in various applications: - **Network Design:** Optimizing paths for minimal cost or maximum efficiency. - **Transportation:** Planning routes and understanding the shortest or safest paths. - **Project Management:** Determining critical paths in task schedules. Understanding weighted graphs is crucial for solving real-world problems that require efficient decision-making based on multiple factors. This example helps illustrate the basic components and usage of weighted graphs.
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