1. Slide 14 - 1 Copyright © 2009 Pearson Education, Inc. AND Active Learning Lecture Slides For use with Classroom Response Systems Chapter 14 Graph Theory

2. Slide 14 - 2 Copyright © 2009 Pearson Education, Inc. In the following graph, determine an Euler circuit. a.CBAECDA b.CBAECDAC c.EABCDA d.AEABCD

3. Slide 14 - 3 Copyright © 2009 Pearson Education, Inc. In the following graph, determine an Euler circuit. a.CBAECDA b.CBAECDAC c.EABCDA d.AEABCD

4. Slide 14 - 4 Copyright © 2009 Pearson Education, Inc. Is it possible for a person to walk through each doorway in the house, whose floor plan is shown below, without using any of the doorways twice? If so, indicate which room the person may start and where he or she will end. a.Yes; A-Gb.Yes; A-C c.Yes; C- Gd.No

5. Slide 14 - 5 Copyright © 2009 Pearson Education, Inc. Is it possible for a person to walk through each doorway in the house, whose floor plan is shown below, without using any of the doorways twice? If so, indicate which room the person may start and where he or she will end. a.Yes; A-Gb.Yes; A-C c.Yes; C- Gd.No

6. Slide 14 - 6 Copyright © 2009 Pearson Education, Inc. Use Fleury’s algorithm to determine an Euler circuit in the following graph. a.BCFAEDA b.DABCFAE c.EDABCFA d.AEDABCFA

7. Slide 14 - 7 Copyright © 2009 Pearson Education, Inc. Use Fleury’s algorithm to determine an Euler circuit in the following graph. a.BCFAEDA b.DABCFAE c.EDABCFA d.AEDABCFA

8. Slide 14 - 8 Copyright © 2009 Pearson Education, Inc. In the following graph, determine a Hamilton path. a.HGEDABCFBE b.GEDABCFH c.HGEDABCF d.FBADEGH

9. Slide 14 - 9 Copyright © 2009 Pearson Education, Inc. In the following graph, determine a Hamilton path. a.HGEDABCFBE b.GEDABCFH c.HGEDABCF d.FBADEGH

10. Slide 14 - 10 Copyright © 2009 Pearson Education, Inc. Alicia lives in Washington, D.C. and wants to take a road trip to visit her friends from college who live in the following cities: New York, Boston, Philadelphia, Dover, and Baltimore. How many ways can Alicia visit each city and return home to Washington, D.C.? a.120b.60 c.25d.24

11. Slide 14 - 11 Copyright © 2009 Pearson Education, Inc. Alicia lives in Washington, D.C. and wants to take a road trip to visit her friends from college who live in the following cities: New York, Boston, Philadelphia, Dover, and Baltimore. How many ways can Alicia visit each city and return home to Washington, D.C.? a.120b.60 c.25d.24

12. Slide 14 - 12 Copyright © 2009 Pearson Education, Inc. Robert decides to take a walk to run his errands. He needs to walk to the drug store, the post office, and the dry cleaners. The distances between these four locations are as follows: home (H) to the drug store (D) is 0.6 miles, home to the post office (P) is 0.5 miles, home to the dry cleaners (C) is 0.7 miles, the drug store to the post office is 0.2 miles, the drug store to the dry cleaner is 0.5 miles, and the dry cleaner to the post office is 0.2 miles. H to D: 0.6H to P: 0.5H to C: 0.7 D to P: 0.2D to C: 0.5C to P: 0.2

13. Slide 14 - 13 Copyright © 2009 Pearson Education, Inc. Represent this traveling salesman problem with a complete, weighted graph. H to D: 0.6H to P: 0.5H to C: 0.7 D to P: 0.2D to C: 0.5C to P: 0.2 a. c. b. d. 0.5 0.2 0.6 0.7 0.2 0.6 0.5 0.2 0.6 0.7 0.2

14. Slide 14 - 14 Copyright © 2009 Pearson Education, Inc. Represent this traveling salesman problem with a complete, weighted graph. H to D: 0.6H to P: 0.5H to C: 0.7 D to P: 0.2D to C: 0.5C to P: 0.2 a. c. b. d. 0.5 0.2 0.6 0.7 0.2 0.5 0.2 0.6 0.7 0.2 0.6

15. Slide 14 - 15 Copyright © 2009 Pearson Education, Inc. Use the brute force method to determine the shortest route for Robert to visit each location once and return home. What is the distance when using this route? a.HDPCH; 1. 7 miles b.HPDCH; 1.7 miles c.HPCD; 1.2 miles d.HCDPH; 1.7 miles

16. Slide 14 - 16 Copyright © 2009 Pearson Education, Inc. Use the brute force method to determine the shortest route for Robert to visit each location once and return home. What is the distance when using this route? a.HDPCH; 1. 7 miles b.HPDCH; 1.7 miles c.HPCD; 1.2 miles d.HCDPH; 1.7 miles

17. Slide 14 - 17 Copyright © 2009 Pearson Education, Inc. Use the nearest neighbor method to approximate the optimal route for Robert to visit each location once and return home. What is the distance when using this route? a.HDPCH; 1. 7 miles b.HPDCH; 1.7 miles c.HPCD; 1.2 miles d.HCDPH; 1.7 miles

18. Slide 14 - 18 Copyright © 2009 Pearson Education, Inc. Use the nearest neighbor method to approximate the optimal route for Robert to visit each location once and return home. What is the distance when using this route? a.HDPCH; 1. 7 miles b.HPDCH; 1.7 miles c.HPCD; 1.2 miles d.HCDPH; 1.7 miles

19. Slide 14 - 19 Copyright © 2009 Pearson Education, Inc. Determine a spanning tree for the graph shown below. a. c. b. d.

20. Slide 14 - 20 Copyright © 2009 Pearson Education, Inc. Determine a spanning tree for the graph shown below. a. c. b. d.

21. Slide 14 - 21 Copyright © 2009 Pearson Education, Inc. Determine the minimum-cost spanning tree for the following weighted graph.

22. Slide 14 - 22 Copyright © 2009 Pearson Education, Inc. a. c. b. d.

23. Slide 14 - 23 Copyright © 2009 Pearson Education, Inc. a. c. b. d.

24. Slide 14 - 24 Copyright © 2009 Pearson Education, Inc. Kathleen is planning on installing a new computer network at her small business. Her current system has computers already in place as shown in the figure below. The numbers are shown in feet.

25. Slide 14 - 25 Copyright © 2009 Pearson Education, Inc. Determine the minimum- cost spanning tree that reaches each computer. a. c. b. d.

26. Slide 14 - 26 Copyright © 2009 Pearson Education, Inc. Determine the minimum- cost spanning tree that reaches each computer. a. c. b. d.

27. Slide 14 - 27 Copyright © 2009 Pearson Education, Inc. If the new networking system materials cost $2.20 per foot, what is the cost of installing the system a.$79.20 b.$83.60 c.$85.80 d.$112.20

28. Slide 14 - 28 Copyright © 2009 Pearson Education, Inc. If the new networking system materials cost $2.20 per foot, what is the cost of installing the system a.$79.20 b.$83.60 c.$85.80 d.$112.20