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NES 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. Which of the following is a Euler path?

Question 2 2. At most, _____ of the verticies will be of an odd degree in a semi-Eulerian graph.

Question 3 3. Which of the following is an Euler path for this graph?

Question 4 4. A complete graph with 3 vertices has how many Hamilton circuits?

Question 5 5. How many vertices does this graph have?

Page 2

Question 6 6. Which vertices can be your starting point?

Question 7 7. How many edges does this graph have?

Question 8 8. Find a Hamilton circuit.

Question 9 9. The best Hamilton circuit in a weighted graph is the one where the total cost is what?

Question 10 10. What can be said about this graph?

Page 3

Question 11 11. How many components does this graph have?

Question 12 12. A complete graph is a graph where each vertex is connected to how many of the other vertices?

Question 13 13. What can be said about this graph?

Question 14 14. What kinds of graphs does Fleury's algorithm work for?

Question 15 15. If a graph has 0 odd vertices, at which vertex must you start?

Page 4

Question 16 16. If a graph has 15 edges, what must the degrees of the vertices add up to?

Question 17 17. What is the shortest path length you can use to get from point 6 to point 2?

Question 18 18. How many vertices in a graph do you visit by traveling a Hamilton path or circuit?

Question 19 19. How many bridges does this graph have?

Question 20 20. If you started at vertex 1, at which vertex will you end up if you are traveling a Hamilton circuit?

Page 5

Question 21 21. A graph with an Euler circuit can have at most how many odd vertices?

Question 22 22. How many vertices can be odd in a Eulerian graph?

Question 23 23. How many times do you visit a vertex when traveling either a Hamilton circuit or path?

Question 24 24. How many Euler circuits are in this graph?

Question 25 25. How many times are you allowed to pass an edge in an Euler path or circuit?

Page 6

Question 26 26. The total number of degrees in a graph is 20. How many edges does it have?

Question 27 27. If vertex 3 is your starting point, which vertex can you not go to?

Question 28 28. Find a Hamilton path.

Question 29 29. How many Euler paths does this graph have?

Question 30 30. How many Euler paths are there in this graph?

NES 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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