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Q1C. Consider the following graph: d b a e g How many vertices are there in the graph How many edges are there in the graph?

Q1C. Consider the following graph: d b a e g How many vertices are there in the graph How many edges are there in the graph?

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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**Q1C. Consider the following graph:** The image above is a graph consisting of several points connected by lines. The points are labeled as vertices: a, b, c, d, e, f, and g. ### Description of the Graph: - **Vertices:** The graph has 7 vertices, each labeled with a letter from a to g. - **Edges:** - Vertex a is connected to b and f. - Vertex b is connected to a, c, and f. - Vertex c is connected to b, d, f, and a. - Vertex d is connected to c, e, and f. - Vertex e is connected to d and g. - Vertex f is connected to a, b, c, d, and g. - Vertex g is connected to f and e. **How many vertices are there in the graph?** [Text Box for Answer] **How many edges are there in the graph?** [Text Box for Answer]
Transcribed Image Text:**Q1C. Consider the following graph:** The image above is a graph consisting of several points connected by lines. The points are labeled as vertices: a, b, c, d, e, f, and g. ### Description of the Graph: - **Vertices:** The graph has 7 vertices, each labeled with a letter from a to g. - **Edges:** - Vertex a is connected to b and f. - Vertex b is connected to a, c, and f. - Vertex c is connected to b, d, f, and a. - Vertex d is connected to c, e, and f. - Vertex e is connected to d and g. - Vertex f is connected to a, b, c, d, and g. - Vertex g is connected to f and e. **How many vertices are there in the graph?** [Text Box for Answer] **How many edges are there in the graph?** [Text Box for Answer]
### Transcription for Educational Use **Question 2B:** Consider the graph with the following vertices and edges: **Vertices (V):** \(\{a, b, c, d, e, f\}\) **Edges (E):** \(\{\{a, b\}, \{a, c\}, \{a, d\}, \{a, f\}, \{b, e\}, \{b, f\}, \{c, d\}, \{d, e\}, \{d, f\}\}\) #### Graph Description The image displays a graph with six vertices labeled \(a, b, c, d, e,\) and \(f\). The edges are drawn between these vertices as follows: - Vertex \(a\) is connected to \(b, c, d,\) and \(f\). - Vertex \(b\) is connected to \(a, e,\) and \(f\). - Vertex \(c\) is connected to \(a\) and \(d\). - Vertex \(d\) is connected to \(a, c, e,\) and \(f\). - Vertex \(e\) is connected to \(b\) and \(d\). - Vertex \(f\) is connected to \(a, b,\) and \(d\). #### Questions 1. **What is the degree of vertex f?** \( \boxed{} \) 2. **What is the total degree of the graph?** \( \boxed{} \) The degree of a vertex is the number of edges incident to it. The total degree of the graph is the sum of the degrees of all vertices.
Transcribed Image Text:### Transcription for Educational Use **Question 2B:** Consider the graph with the following vertices and edges: **Vertices (V):** \(\{a, b, c, d, e, f\}\) **Edges (E):** \(\{\{a, b\}, \{a, c\}, \{a, d\}, \{a, f\}, \{b, e\}, \{b, f\}, \{c, d\}, \{d, e\}, \{d, f\}\}\) #### Graph Description The image displays a graph with six vertices labeled \(a, b, c, d, e,\) and \(f\). The edges are drawn between these vertices as follows: - Vertex \(a\) is connected to \(b, c, d,\) and \(f\). - Vertex \(b\) is connected to \(a, e,\) and \(f\). - Vertex \(c\) is connected to \(a\) and \(d\). - Vertex \(d\) is connected to \(a, c, e,\) and \(f\). - Vertex \(e\) is connected to \(b\) and \(d\). - Vertex \(f\) is connected to \(a, b,\) and \(d\). #### Questions 1. **What is the degree of vertex f?** \( \boxed{} \) 2. **What is the total degree of the graph?** \( \boxed{} \) The degree of a vertex is the number of edges incident to it. The total degree of the graph is the sum of the degrees of all vertices.
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