Name:___________________
Date:_____________
Discrete Quiz Ch.2
1. Which of the following describes a Hamiltonian circuit for the graph below?
A)
B)
C)
D)
Ans:
ABCDEFJIHG
ABCDEAFJDIHBGFEJICHGA
ABCDEAGHIJFA
AEDCBGHIJFA
D
2. Which of the following describes a Hamiltonian circuit for the graph below?
A)
B)
C)
D)
Ans:
ABCDEFGA
ACBAEGFDEA
ACBFGDEA
ABCDGEF
C
3. On the graph below, which routing is produced by using the nearest-neighbor algorithm
to solve the traveling salesman problem?
A)
B)
C)
D)
Ans:
ABCDA
ABDCA
ACBDA
ABCD
B
4. For the graph below, what is the cost of the Hamiltonian circuit obtained by using the
nearest-neighbor algorithm, starting at A?
A)
B)
C)
D)
Ans:
60
54
62
66
D
5. Which path listed forms a Hamiltonian circuit on the graph below?
A)
B)
C)
D)
Ans:
ADCBFGHEA
ABCDHGFE
ABCDHGFEA
ABCDHGFEHDA
C
6. On a map there are roads from town A of length 10, 26, 12, and 50 miles. Using the
nearest-neighbor algorithm for finding a Hamiltonian circuit starting at town A, which
road would be traveled first?
A) road of length 10
B) road of length 26
C) road of length 12
D) road of length 50
Ans: A
7. For the traveling salesman problem (Hamiltonian circuit) applied to six cities, how
many tours are possible?
A) 60
B) 120
C) 360
D) 720
Ans: B
8. For the traveling salesman problem (Hamiltonian circuit) applied to five cities, how
many unique tours are possible?
A) 120
B) 60
C) 24
D) 12
Ans: D
9. For the traveling salesman problem applied to seven cities, how many
unique tours are possible?
A) 360
B) 720
C) 2520
D) 5040
Ans A
10. A connected graph G has 32 vertices. How many vertices does a spanning tree of G
have?
A) 30
B) 31
C) 32
D) 33
Ans: C
11. On the graph below, which routing is produced by using the sorted-edges algorithm to
solve the traveling salesman problem?
A)
B)
C)
D)
Ans:
ABCDA
ABDCA
ACBDA
ABCD
A
12.
For the graph below, what is the cost of the Hamiltonian circuit obtained by using
the sorted-edges algorithm?
A)
B)
C)
D)
Ans:
220
225
235
295
C
13. For the graph below, which routing is produced by using the sorted-edges algorithm to
solve the traveling salesman problem?
A)
B)
C)
D)
Ans:
ACBEDA
ABCEDA
ABEDCA
ADCEBA
A
14. Use Kruskal's algorithm for minimum-cost spanning trees on the graph below. The cost
of the tree found is:
A)
B)
C)
D)
Ans:
5
9
12
15
B
15. Use Kruskal's algorithm for minimum-cost spanning trees on the graph below. The cost
of the tree found is:
A)
B)
C)
D)
Ans:
23
20
16
5
C
16. Use Kruskal's algorithm for minimum-cost spanning trees on the graph below. The cost
of the tree found is:
A)
B)
C)
D)
Ans:
47
25
22
15
C
17. If the order-requirement digraph for a collection of tasks is shown below, then what is
the minimum completion time for the collection of tasks?
A)
B)
C)
D)
Ans:
64 minutes
43 minutes
36 minutes
28 minutes
B
18. What is the earliest possible completion time for a job whose order-requirement
digraph is shown below?
A)
B)
C)
D)
Ans:
15
22
34
19
D
19. The nearest-neighbor algorithm for solving the traveling salesman problem always
produces the same result as the sorted-edges algorithm.
A) True
B) False
Ans: B
20. When Kruskal's algorithm is used to find a minimum-cost spanning tree on a graph,
which of the following is false?
A) Circuits are not permitted in the tree.
B) The tree contains the edge of the graph of minimum cost.
C) The tree is not necessarily connected.
D) The tree may contain the edge of the highest cost.
Ans: C
21. A spanning tree of a graph must contain every edge of the graph.
A) True
B) False
Ans: B
22. A digraph is a graph with exactly two vertices.
A) True
B) False
Ans: B
23. The graph below shows the cost (in hundreds of dollars) of installing telephone wires
between the work spaces in an office complex. Use Kruskal's algorithm for minimumcost spanning trees to find the cost for establishing this phone network.
A)
B)
C)
D)
Ans:
$2100
$2400
$2900
$6200
B
24. Given the two graphs shown below, which one represents a tree?
A)
B)
C)
D)
Ans:
I only
II only
Both I and II
Neither I nor II
B
25. Kris has 3 pairs of pants of different colors, 5 shirts of different colors, and 2 pairs of
shoes. How many different outfits can Kris create?
A) 2
B) 10
C) 30
D) 50
Ans: C