Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
**Graph Exercise:** 1) **Problem Statement:** Find the degree of each vertex in the following graph. **Graph Description:** The graph displayed consists of seven vertices, forming a hexagon with an additional central vertex. The vertices are connected as follows: - Each vertex of the hexagon is connected to the two adjacent vertices, forming the outer hexagon. - The central vertex is connected to each of the vertices of the hexagon. - Additional lines connect some vertices in the hexagon directly across, forming an internal star-like pattern within the hexagon. **Degree of Vertices:** To solve the exercise, you need to count the number of edges connected to each vertex. - **Outer Hexagon Vertices:** Each of these vertices is connected to three other vertices in the pattern (two adjacent vertices plus the central vertex). - **Central Vertex:** This vertex is connected to all six vertices of the hexagon. Understanding these connections will allow you to determine the degree for each vertex in the graph.
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Transcribed Image Text:**Graph Exercise:** 1) **Problem Statement:** Find the degree of each vertex in the following graph. **Graph Description:** The graph displayed consists of seven vertices, forming a hexagon with an additional central vertex. The vertices are connected as follows: - Each vertex of the hexagon is connected to the two adjacent vertices, forming the outer hexagon. - The central vertex is connected to each of the vertices of the hexagon. - Additional lines connect some vertices in the hexagon directly across, forming an internal star-like pattern within the hexagon. **Degree of Vertices:** To solve the exercise, you need to count the number of edges connected to each vertex. - **Outer Hexagon Vertices:** Each of these vertices is connected to three other vertices in the pattern (two adjacent vertices plus the central vertex). - **Central Vertex:** This vertex is connected to all six vertices of the hexagon. Understanding these connections will allow you to determine the degree for each vertex in the graph.
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