1. Is the following graph Hamiltonian- connected from vertex v? a). Yes b). No c). I have absolutely no idea v

2. Is the following graph Hamiltonian- connected from vertex v? a). Yes b). No c). I have absolutely no idea v

3. Is the following graph Hamiltonian- connected from vertex v? a). Yes b). No c). I have absolutely no idea v

4. What is the next line of the proof? a). Let G be a graph with k vertices. b). Assume the theorem holds for all graphs with k+1 vertices. c). Let G be a graph with k+1 vertices. d). Assume the theorem holds for all graphs with k-1 vertices. e). Let G be a graph with k-1 vertices.

5. What is the next line of the proof? a). Add a vertex to G to create G’. b). Delete a vertex from G to create G’. c). Add an edge to G to create G’. d). Delete an edge from G to create G’.

6. What is the next line of the proof? a). Assume G is a tree. b). Assume G is not a tree. c). Assume q  p – 1. d). Assume if q = p – 1, then G is a tree.

7. What is the next line of the proof? a). Then every tree must be connected. b). Then G is not connected. c). Then q  p – 1. d). Then G contains a cycle.

8. How many different spanning trees does the given graph have? a). 0 b). 1 c). 2 d). 3 e). 4 f). 5 g). 6 h). 7 i). 8