SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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Lionel Perry
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1 Chapter 6 Test Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 1) The number of edges in K12 is 1) 2) The number of Hamilton circuits in K12 is 2) 3) The number of edges in the complete graph with 50 vertices is 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) n! = A) n (n - 1)! B) n! + (n - 1)! C)n! (n - 1)! D) n + (n - 1)! 4) 5) (n- 1)! = n! A) (n- 1)! B) n! - 1! C) n! n D) n (n - 1)! 5) 6) 101! 100! = A) 101 B) 10,100 C) 1.01 D) 1 6) 7) If 99! 10156, which of the following numbers most closely approximates 100!? A) B) C) D) ) 1

2 8) 26! + 24! 25! A) 50! 25! = B) 25 C) D) 2 9) In a complete graph with 12 vertices (A through L), the total number of Hamilton paths that start at vertex A and end at vertex L is A) 11!. B) 12!. C)10!. D) 13!. 8) 9) 10) In a complete graph with 16 vertices (A through P), the total number of Hamilton paths that start at vertex A, pass through vertex D after traversing exactly three edges, and end at vertex P is A) 13! B) 16! C)3! 12! D) 14! 10) 11) In a complete graph with 720 distinct Hamilton circuits, there is a total of A) 9 vertices. B) 6 vertices. C) 7 vertices. D) 5 vertices. 11) 12) A Hamilton circuit for the following graph 12) A) must contain the edge CD. B) must contain the edge FE. C)must contain the edge AB. D) All of the above 2

3 13) The following graph 13) A) has several Hamilton circuits, none of which contain the edge BD. B) has a single Hamilton circuit (and its mirror-image circuit). C) has no Hamilton circuit. D) has several Hamilton circuits, all of which contain the edge CG. A delivery truck must deliver furniture to 4 different locations (A, B, C, and D). The trip must start and end at A. The graph below shows the distances (in miles) between locations. We want to minimize the total distance traveled. 14) The nearest-neighbor algorithm applied to the graph yields the following solution: A) A, B, D, C, A. B) A, D, B, C, A. C)A, D, C, B, A. D) A, C, B, D, A. 14) A truck must drop off furniture at 4 different homes (A, B, C, and D) as shown in the graph below, starting and ending at A. The numbers on the edges represent distances (in miles) between locations. The truck driver wants to minimize the total length of the trip. 15) The length of the trip of the circuit found using the nearest-neighbor algorithm is: A) 17 miles. B) 16 miles. C)22 miles. D) 19 miles. 15) 3

4 16) The cheapest-link algorithm applied to the graph yields the following solution: A) A, C, D, B, A. B) A, B, D, C, A. C)A, C, B, D, A. D) A, D, C, B, A. 16) 17) The length of the trip of the circuit found using the cheapest-link algorithm is A) 19 miles. B) 22 miles. C)29 miles. D) 17 miles. 17) 18) The repetitive nearest-neighbor algorithm applied to the graph yields the following solution: A) A, B, D, C, A. B) A, C, D, B, A. C)A, D, C, B, A. D) A, C, B, D, A. 18) 19) The length of the trip of the circuit found using the repetitive nearest-neighbor algorithm is: A) 17 miles. B) 16 miles. C)19 miles. D) 22 miles. 19) 20) An optimal solution to this problem is given by A) A, C, D, B, A. B) A, B, D, C, A. C)A, D, B, C, A. D) A, B, C, D, A. 20) 4

5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. A traveling salesman's territory consists of the 5 cities shown on the following mileage chart. The salesman must organize a round trip that starts and ends at Louisville (his hometown) and will pass through each of the other four cities exactly once. Mileage Chart 21) The nearest-neighbor algorithm applied to this problem yields the following solution: 21) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 22) The cheapest-link algorithm applied to this problem yields the following solution: A) Louisville, Boston, Buffalo, Chicago, Columbus, Louisville. B) Louisville, Columbus, Chicago, Buffalo, Boston, Louisville. C) Louisville, Columbus, Buffalo, Boston, Chicago, Louisville. D) Louisville, Chicago, Buffalo, Boston, Columbus, Louisville. 22) 23) The repetitive nearest-neighbor algorithm applied to this problem yields the following solution: A) Louisville, Columbus, Chicago, Buffalo, Boston, Louisville. B) Louisville, Boston, Buffalo, Chicago, Columbus, Louisville. C) Louisville, Chicago, Buffalo, Boston, Columbus, Louisville. D) Louisville, Columbus, Buffalo, Boston, Chicago, Louisville. 23) 24) At an average cost of 25 cents per mile, the cheapest possible trip that starts at Louisville and passes through each of the other cities exactly once would cost A) $ B) $ C) $ D) $ ) 25) At an average cost of 50 cents per mile, the cheapest possible trip that starts at Louisville and passes through each of the other cities exactly once would cost A) $ B) $ C) $ D) $ ) 5

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Chapter 7 & 8 Test Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Which of the following four graphs is a tree?