https://file.aiquickdraw.com/mathbot/file/1729467518926ck5q7quw.pdf

It seems like you've uploaded a quiz on graph theory from MAT 109. Here are the questions from the document:

1. **For the given graph (network), answer the following:**
   a) What is deg(E)?
   b) What is deg(A)?
   c) What is the sum of the degrees of all the vertices in the graph?
   d) How many edges does the graph have?
   e) Is there a circuit in the graph that starts at C? If so, list one.
   f) List one path from vertex E to vertex D that travels through F.
   g) List all vertices adjacent to vertex F.
   h) Does this graph have any bridges? If so, list them.

2. **In a graph with 15 edges and 5 vertices (A, B, C, D, E), given:**
   - deg(A) = 3, deg(B) = 6, deg(C) = 9, deg(D) = 2
   - Find the degree of vertex E. (You don’t need to draw the graph).

Would you like to start solving a specific question, or do you need an explanation on a particular topic related to graph theory?

Here are 5 related questions:
1. What is the relationship between the degree of a vertex and the number of edges in a graph?
2. How can you determine if a graph has a circuit?
3. What are bridges in a graph, and why are they significant?
4. How is the sum of vertex degrees related to the number of edges?
5. What are paths and circuits in a graph?

**Tip:** The sum of the degrees of all vertices in a graph is always twice the number of edges.

Given the graph (network), answer the following: What is deg(E)? What is deg(A)? What is the sum of the degrees of all the vertices? How many edges does the graph have? Is there a circuit that starts at C? List a path from E to D that passes through F. List all vertices adjacent to F. Are there any bridges in the graph? Additionally, in a graph with 15 edges and 5 vertices (A, B, C, D, E), find the degree of vertex E given that deg(A) = 3, deg(B) = 6, deg(C) = 9, and deg(D) = 2.

Solve graph theory problems, including finding the degree of vertices, identifying circuits, paths, and bridges, and calculating the total number of edges using the sum of vertex degrees. Suitable for college-level students in introductory graph theory courses.

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