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.