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# NMTA Math: Graph Theory Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. How many odd vertices can a graph have in order to use Fleury's algorithm?

#### Question 2 2. How many Euler paths does this graph have?

#### Question 3 3. A complete graph is a graph where each vertex is connected to how many of the other vertices?

#### Question 4 4. If a graph has 0 odd vertices, at which vertex must you start?

#### Question 5 5. What can be said about this graph?

### Page 2

#### Question 6 6. A graph with an Euler circuit can have at most how many odd vertices?

#### Question 7 7. If vertex 3 is your starting point, which vertex can you not go to?

#### Question 8 8. How many edges does this graph have?

#### Question 9 9. How many components does this graph have?

#### Question 10 10. At most, _____ of the verticies will be of an odd degree in a semi-Eulerian graph.

### Page 3

#### Question 11 11. What kinds of graphs does Fleury's algorithm work for?

#### Question 12 12. A complete graph with 6 vertices has how many Hamilton circuits?

#### Question 13 13. Which vertices can be your starting point?

#### Question 14 14. Which of the following is an Euler path for this graph?

#### Question 15 15. How many bridges does this graph have?

### Page 4

#### Question 16 16. Which of the following is a Hamilton circuit?

#### Question 17 17. How many vertices does this graph have?

#### Question 18 18. Find a Hamilton circuit.

#### Question 19 19. The start and end points must be which two vertices?

#### Question 20 20. How many vertices in a graph do you visit by traveling a Hamilton path or circuit?

### Page 5

#### Question 21 21. Which of the following is a Euler path?

#### Question 22 22. How many Euler circuits are in this graph?

#### Question 23 23. The best Hamilton circuit in a weighted graph is the one where the total cost is what?

#### Question 24 24. If you started at vertex 1, at which vertex will you end up if you are traveling a Hamilton circuit?

#### Question 25 25. The total number of degrees in a graph is 20. How many edges does it have?

### Page 6

#### Question 26 26. How many Euler paths are there in this graph?

#### Question 27 27. What can be said about this graph?

#### Question 28 28. How many times are you allowed to pass an edge in an Euler path or circuit?

#### Question 29 29. How many times do you visit a vertex when traveling either a Hamilton circuit or path?

#### Question 30 30. A graph with an Euler path can have at most how many odd vertices?

#### NMTA Math: Graph Theory Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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