1) Find the degree of each vertex in the following graph
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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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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