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Integrated Math 2 Section 8-6

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Directed Graphs

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Integrated Math 2 Section 8-6

  1. 1. Section 8-6 Directed Graphs
  2. 2. Essential Question • How do you use a picture, diagram, or model to represent a real-world problem? • Where you’ll see this: • Sports, navigation, business
  3. 3. Directed Graph
  4. 4. Directed Graph A geometrical representation of a map
  5. 5. Directed Graph A geometrical representation of a map A collection of points and arrows to show relationships
  6. 6. Example 1 In the diagram, A-G represent students, and the arrows in the directed graph indicate that one person knows the other person’s phone number. A B C D E F G
  7. 7. Example 1 How many phone numbers does B know? A B C D E F G
  8. 8. Example 1 How many phone numbers does B know? A B C D E F G
  9. 9. Example 1 How many phone numbers does B know? A B C D E F G B knows three numbers
  10. 10. Example 1 If E wanted to call G, how many calls would E have to make to get G’s number? A B C D E F G
  11. 11. Example 1 If E wanted to call G, how many calls would E have to make to get G’s number? A B C D E F G
  12. 12. Example 1 If E wanted to call G, how many calls would E have to make to get G’s number? A B C D E F G
  13. 13. Example 1 If E wanted to call G, how many calls would E have to make to get G’s number? A B C D E F G E needs to make 2 calls to get G’s number
  14. 14. Example 1 What is the total number of direct calls that can be made in this system? A B C D E F G
  15. 15. Example 1 What is the total number of direct calls that can be made in this system? A B C D E F G 11 total direct calls can be made
  16. 16. Example 1 Create a matrix to describe this problem. Let 0 = the cannot call that person and 1 = they can make that call. A B C D E F G
  17. 17. Example 1 A B C D E F G
  18. 18. Example 1 A B C D E To F G A B C D E F G A    B  C  From   D  E    F  G   
  19. 19. Example 1 A B C D E To F G A B C D E F G A 0    B 0  C 0  From   D 0  E 0    F 0  G 0 
  20. 20. Example 1 A B C D E To F G A B C D E F G A 0 1 1 0 0 0 0   B 0  C 0  From   D 0  E 0    F 0  G 0 
  21. 21. Example 1 A B C D E To F G A B C D E F G A 0 1 1 0 0 0 0   B 0 0 1 1 1 0 0 C 0  From   D 0  E 0    F 0  G 0 
  22. 22. Example 1 A B C D E To F G A B C D E F G A 0 1 1 0 0 0 0   B 0 0 1 1 1 0 0 C 0 0 0 0 0 1 1 From   D 0 1 0 0 1 0 0 E 0 1 0 1 0 0 0   F 0 0 0 0 0 0 0 G 0  0 0 0 0 0 0 
  23. 23. Homework
  24. 24. Homework p. 359 #1-12 “Don’t worry about the world coming to an end today. It’s already tomorrow in Australia.” - Charles M. Schulz

Directed Graphs

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