1. What is the first line of the proof? a). Assume G has an Eulerian circuit. b). Assume every vertex has even degree. c). Let v be any vertex in G. d). Let v be a vertex of odd degree.

2. What is the second line of the proof? a). Assume G has an Eulerian circuit. b). Assume every vertex has even degree. c). Let v be any vertex in G. d). Let v be a vertex of odd degree.

3. How many edges need to be repeated in order to walk around the graph shown and include every edge at least once? 0 1 2 3 4 5 6 7 8

4. How many edges need to be repeated in order to walk around the graph shown and include every edge at least once? 0 1 2 3 4 5 6 7 8

5. How many edges need to be repeated in order to walk around the graph shown and include every edge at least once? 0 1 2 3 4 5 6 7 8

6. How many edges need to be repeated in order to walk around the graph shown and include every edge at least once? 0 1 2 3 4 5 6 7 8

7. How many edges need to be repeated in order to walk around the graph shown and include every edge at least once? a). 0 b). 1 c). 2 d). 3 e). 4 f). 5 g). 6 h). 7 i). 8

8. Does the graph shown have a Hamilton cycle? a). Yes b). No

9. Does the graph shown have a Hamilton cycle? a). Yes b). No

10. Does the graph shown have a Hamilton cycle? a). Yes b). No

11. Does the graph shown have a Hamilton cycle? a). Yes b). No

12. Does the graph shown have a Hamilton cycle? a). Yes b). No

13. Does the graph shown have a Hamilton cycle? a). Yes b). No