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1. How many vertices in the graph below have odd valences?
0
d. 4
ANSWER: c
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 5/11/2022 11:16 AM
CUSTOM ID: question_1239779_6217f735bf264
2. On a graph that represents six cities and the roads between them, the valence of vertex A is 4. What does this mean in real-world terms?
ANSWER: If the valence of vertex A is 4, it means there are four roads that lead to town A.
RATIONALE: If the valence of vertex A is 4, it means there are four roads that lead to town A.
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239780_6217f735eae5a
3. What is the valence of vertex A in the graph below?
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 5/11/2022 10:42 AM
CUSTOM ID: question_1239784_6217f73642554
4. A graph that represents six cities and the roads among them is connected. What does this mean in real-world terms?
ANSWER: Any pair of two cities has at least one connecting path of roads.
RATIONALE: Any pair of two cities has at least one connecting path of roads.
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239782_6217f7361ae08
5. What is the valence of vertex A in the graph below?
Name: Class: Date:
ANSWER: d
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 5/11/2022 11:17 AM
CUSTOM ID: question_1239783_6217f7361b16e
6. Describe the two conditions for a graph to have an Euler circuit.
ANSWER: The graph must be connected and have all valences even.
RATIONALE: The graph must be connected and have all valences even.
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239785_6217f73663a3e
7. Draw a graph representing four cities, A, B, C, and D, with a road that connects each pair of cities given: AB, AC, BC, BD, CD.
ANSWER:
RATIONALE:
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239786_6217f73663e2d
8. What is the valence of vertex A in the graph below?
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239787_6217f7368d102
9. How many vertices in the graph below have even valences?
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 5/11/2022 11:16 AM
CUSTOM ID: question_1239781_6217f735eb1bf
10. What is the valence of vertex B in the graph below?
ANSWER: d
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239788_6217f736a6b56
Chapter 1
11. Which of the following defines the valence of vertex A of a graph?
a. The total number of vertices of the graph
b. The number of edges meeting at vertex A
c. The total number of edges of the graph
d. None of the above
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239789_6217f736ca735
12. Draw a graph with vertices A, B, C, and D in which the valence of vertices A and D is 3 and the valence of vertices B and C is 2.
ANSWER: Answers may vary. One solution is:
RATIONALE: Answers may vary. One solution is:
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239790_6217f736cab3d
13. What is the sum of all valences of the graph shown below?
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ANSWER: d
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239791_6217f7370974a
14. Draw a graph that has four vertices, with valences 1, 2, 3, and 4.
ANSWER:
RATIONALE:
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
Name: Class: Date:
Chapter 1
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239792_6217f737267b2
15. Draw a graph with vertices A, B, and C in which vertex A has valence 4 and vertices B and C have valence 5.
ANSWER:
RATIONALE:
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
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Name: Class:
Chapter 1
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239793_6217f7374a825
16. Which of the graphs below are connected?
a. I only
b. II only
c. Both I and II
d. Neither I nor II
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 5/11/2022 11:18 AM
CUSTOM ID: question_1239794_6217f7376b7b0
17. Which of the graphs below are connected?
a. I only
b. II only
c. Both I and II
d. Neither I nor II
ANSWER: c
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
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Chapter 1
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239795_6217f7378f835
18. Which of the graphs below are connected?
a. I only
b. II only
c. Both I and II
d. Neither I nor II
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239796_6217f737b0d79
19. Consider the path represented by the sequence of numbered edges on the graph below. Explain why the path is not an Euler circuit.
ANSWER: The path is not an Euler circuit because it does not start and stop at the same vertex.
RATIONALE: The path is not an Euler circuit because it does not start and stop at the same vertex.
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239797_6217f737cfcb4
20. Which of the following statements about a connected graph is always true?
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Chapter 1
a. Every pair of vertices is joined by a single edge.
b. A path of edges exists between any two vertices of the graph.
c. There is an even number of vertices on the graph.
d. There is an even number of edges on the graph.
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239798_6217f737e2d89
21. A graph that is not connected must have at least one vertex with valence 0.
a. True
b. False
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239799_6217f737e3119
22. If a graph of four vertices has a vertex with valence 0, then the graph is not connected.
a. True
b. False
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239800_6217f737e3474
23. If a graph of six vertices is connected, then there are at least five edges.
a. True
b. False
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Name: Class: Date:
Chapter 1
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239801_6217f737e37cc
24. Which of the graphs below have Euler circuits?
a. I only
b. II only
c. Both I and II
d. Neither I nor II
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 5/11/2022 11:53 AM
CUSTOM ID: question_1239802_6217f737e3b28
25. Which of the graphs below have Euler circuits?
a. I only
b. II only
c. Both I and II
d. Neither I nor II
ANSWER: c
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
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Chapter 1
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239803_6217f73814761
26. Which of the graphs below have Euler circuits?
a. I only
b. II only
c. Both I and II
d. Neither I nor II
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239804_6217f73832f46
27. Which of the graphs below have Euler circuits?
a. I only
b. II only
c. Both I and II
d. Neither I nor II
ANSWER: d
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239805_6217f73855b1e
Name: Class: Date:
Chapter 1
28. Consider the path represented by the sequence of numbered edges on the graph below. Explain why the path is not an Euler circuit.
ANSWER: The path is not an Euler circuit because it does not cover every edge of the graph.
RATIONALE: The path is not an Euler circuit because it does not cover every edge of the graph.
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239806_6217f7387b006
29. Draw a graph with eight vertices, with the valence of each vertex being even, that does not have an Euler circuit.
ANSWER: Answers may vary. One solution is:
RATIONALE: Answers may vary. One solution is:
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239807_6217f73897fe3
30. Which of the graphs below have Euler circuits?
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a. I only
b. II only
c. Both I and II
d. Neither I nor II
ANSWER: d
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239808_6217f738b7973
31. An Euler circuit of a graph passes through each vertex exactly once.
a. True
b. False
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239809_6217f738d33e7
32. Every graph with an Euler circuit has an even number of edges.
a. True
b. False
Name: Class: Date:
Chapter 1
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239810_6217f738d3762
33. Every graph that has an Euler circuit is connected.
a. True
b. False
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239811_6217f738d3abb
34. Every connected graph has an Euler circuit.
a. True
b. False
ANSWER: b
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239812_6217f738d3e0f
35. Every graph with an Euler circuit has only vertices with even valences.
a. True
b. False
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
Copyright Macmillan Learning. Powered by Cognero. Page 16
Name: Class: Date:
Chapter 1
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239813_6217f738d415c
36. It is possible for a graph with all vertices of even valence to NOT have an Euler circuit.
a. True
b. False
ANSWER: a
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239814_6217f738d44df
37. Explain why the graph shown below does not have an Euler circuit.
ANSWER: The graph does not have an Euler circuit because the valences of vertex B and vertex D are odd.
RATIONALE: The graph does not have an Euler circuit because the valences of vertex B and vertex D are odd.
POINTS: 1
REFERENCES: Chapter: 1
QUESTION TYPE: Essay
HAS VARIABLES: False
STUDENT ENTRY MODE: Complete
DATE CREATED: 2/24/2022 4:23 PM
DATE MODIFIED: 2/24/2022 4:23 PM
CUSTOM ID: question_1239815_6217f738d47ce
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