https://file.aiquickdraw.com/mathbot/file/1729613803307m0ex2rbz.pdf

The document you uploaded appears to be a quiz from a course called MAT 109. The quiz focuses on graph theory, with questions about vertex degrees, edges, paths, and circuits in a graph.

Here’s a brief summary of the questions:

1. **Graph Properties:**
   - a) Degree of vertex \( E \).
   - b) Degree of vertex \( A \).
   - c) Sum of the degrees of all vertices in the graph.
   - d) Number of edges in the graph.
   - e) Whether there's a circuit starting at vertex \( C \) (if so, list one).
   - f) A path from vertex \( E \) to vertex \( D \) through \( F \).
   - g) Vertices adjacent to \( F \).
   - h) Whether the graph has any bridges (if so, list them).

2. **Graph with 15 Edges and 5 Vertices:**
   - Given degrees of four vertices, determine the degree of vertex \( E \).

Would you like help with solving these questions? If so, I can guide you through each one.

Here are some possible related questions:
1. What is the degree of a vertex in graph theory?
2. How do you calculate the total number of edges in a graph from vertex degrees?
3. What is a circuit in a graph, and how is it different from a path?
4. How do you determine if a graph has a bridge?
5. What are adjacent vertices?

**Tip:** In any simple graph, the sum of all vertex degrees is equal to twice the number of edges.

Given the graph (network) provided, answer the following questions: What is the degree of vertex E? What is the degree of vertex A? What is the sum of the degrees of all the vertices? How many edges are in the graph? Is there a circuit starting at vertex C? List one path from E to D through F. List adjacent vertices of F. Are there any bridges in the graph? A graph has 15 edges and 5 vertices. Given degrees for vertices A, B, C, and D, what is the degree of vertex E?

This quiz from MAT 109 focuses on fundamental graph theory questions including vertex degrees, paths, circuits, and bridges. It challenges students to calculate the degree of vertices, identify circuits, and explore graph connectivity. Ideal for college-level students studying introductory graph theory.

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