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16 Multiple Choice solved Questions, Introduction to Contemporary Math | MATH 113, Exams of Mathematics

Southern Illinois University (SIU) - CarbondaleMathematics
Prof. Mingqing Xiao

Material Type: Exam; Professor: Xiao; Class: Intro Contemporary Math; Subject: Mathematics; University: Southern Illinois University Carbondale; Term: Spring 2009;

Typology: Exams

2009/2010

Uploaded on 02/24/2010

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Math 113-Sections 21−26 Review Sheet for Exam 1 Spring 2009
Choose the most appropriate answer among the choices A), B), C), and D).
Page 1
1.
What is the valence of vertex A in the graph below?
A)
2
B) 3
C)
4
D)
5
2.
Which of the graphs below are connected?
A)
I only
B) II only
C)
Both I and II
D)
Neither I nor II
3.
Which of the graphs below have Euler circuits?
A)
I only
B) II only
C)
Both I and II
D)
Neither I nor II
pf3
pf4
pf5

Partial preview of the text

Download 16 Multiple Choice solved Questions, Introduction to Contemporary Math | MATH 113 and more Exams Mathematics in PDF only on Docsity!

Math 113-Sections 21− 26 Review Sheet for Exam 1 Spring 2009

Choose the most appropriate answer among the choices A), B), C), and D).

  1. What is the valence of vertex A in the graph below?

A) 2

B) 3

C) 4

D) 5

  1. Which of the graphs below are connected?

A) I only B) II only C) Both I and II D) Neither I nor II

  1. Which of the graphs below have Euler circuits?

A) I only B) II only C) Both I and II D) Neither I nor II

  1. Consider the paths represented by the numbered sequence of edges on the graphs below. Which path represents an Euler circuit?

A) I only B) II only C) Both I and II D) Neither I nor II

  1. For which of the two situations below is it desirable to find an Euler circuit or an efficient eulerization of a graph? I. A pizza delivery person takes pizzas to ten houses in a neighborhood and then returns to pick up the next set to be delivered. II. A postal carrier picks up mail from six collection boxes around a city. A) I only B) II only C) Both I and II D) Neither I nor II
  2. In order to eulerize the graph below, give the fewest number of edges that need to be duplicated?

A) 4

B) 6

C) 10

D) 12

  1. Which of the following describes a Hamiltonian circuit for the graph below?

A) ABCDEFJIHG

B) ABCDEAFJDIHBGFEJICHGA

C) ABCDEAGHIJFA

D) AEDCBGHIJFA

  1. For the graph below, what is the cost of the Hamiltonian circuit obtained by using the nearest-neighbor algorithm, starting at A?

A) 60

B) 54

C) 62

D) 66

  1. For the traveling salesman problem applied to seven cities, how many distinct tours are possible? A) 360 B) 720 C) 2520 D) 5040
  2. For the graph below, what is the cost of the Hamiltonian circuit obtained by using the sorted-edges algorithm?

A) 40

B) 58

C) 60

D) 66

  1. Which of the following is a correct vertex coloring of the given graph? (Capital letters indicate which color the vertex is colored.)

A) I only B) II only C) Both I and II D) Neither I nor II

Answer Key

1. C

2. A

3. C

4. B

5. D

6. B

  1. b
  2. B
  3. D
  4. D
  5. A
  6. D
  7. C
  8. C
  9. C
  10. C