2. 1) Find and label the degree of each vertex in the graph.

3. 2) List all bridges in the graph below.

4. 3) Determine whether the graph below has an Euler path, an Euler circuit, or neither. If it has an Euler path or Euler circuit, state which one and describe the sequence used to create it.

5. 4) Draw a graph that models the connecting relationships in the floor plan using vertices as rooms and edges as doors. Is it possible to find a path that uses each door exactly once? If it is possible, where should this path begin?

6. 5) Find two Hamilton circuits in the graph below. One circuit should start at F and end with D, F. The second circuit should start at C.

7. 6) Find the optimal (least expensive) Hamilton circuit that begins at vertex A in the graph below. What is the total weight of that Hamilton circuit?

8. 7) Find the minimum spanning tree for the weighted graph below. Give the total weight of the minimum spanning tree.