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Graph Theory: Traveling Salesman Problem (TSP)

Graph Theory: Traveling Salesman Problem (TSP). E 3 Teacher Summer Research Program 2005 Texas A & M University. June 29, 2005. TAKS Objectives 9 th & 10 th Grade. Objective 1 – Ab1A, B, C, D & E Objective 2 – Ab2A & D, Ab3A & B Objective 3 – Ac1A & C Objective 6 – 8.7D

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Graph Theory: Traveling Salesman Problem (TSP)

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  1. Graph Theory:Traveling Salesman Problem (TSP) E3 Teacher Summer Research Program 2005 Texas A & M University June 29, 2005

  2. TAKS Objectives9th & 10th Grade Objective 1 – Ab1A, B, C, D & E Objective 2 – Ab2A & D, Ab3A & B Objective 3 – Ac1A & C Objective 6 – 8.7D Objective 10 - 8.14A, B & C, 8.15A, 8.16A & B

  3. Material • GEO Board • Yarn • Rubber bands • Colored pencils • Grid paper • Graphing calculator

  4. Vocabulary • Nodes (vertices) • Edges (arcs) • Degree • Adjacent • Path

  5. Vocabulary • Length • Circuit • Simple Graph • Complete Graph

  6. Nodes (vertices)

  7. Nodes (vertices) • Land • Phone numbers • People • Junction points (electric circuits) • Atom • Chess players • Companies or industries

  8. Edges (arcs)

  9. Edges (arcs) • Bridges connecting land • Calls made from one number to another connecting phone numbers • Relationships or acquaintances connecting by people • Wires connecting junction points (electric circuits) • Bonds between atoms connecting atoms • Matches connecting chess players (chess tournament) • Transactions connecting companies or industries

  10. Degree B A C D H G E F

  11. Degree • Node A is of two degrees • Node B is of two degrees • Node C is of six degrees • Node D is of three degrees • How many degrees are nodes E, F, G and H?

  12. Adjacent B A C D H G E F

  13. Adjacent • Node A is adjacent to Nodes C and H • Node B is adjacent to Nodes F and H • Node C is adjacent to Nodes A, D, E, F, G and H • Node D is adjacent to Nodes C, E and H • What nodes are adjacent to nodes E, F, G and H?

  14. Path E A D F B C

  15. Path E A D F B C

  16. Path E A D F B C

  17. No Path E A D F B C

  18. Draw two different paths. E A D F B C

  19. E Length D A F B C

  20. E Length D A F B C

  21. E Length D A F B C

  22. E Length D A F B C

  23. CircuitPoint A is the starting point A E B D C

  24. CircuitPoint A is the starting point A E B D C

  25. CircuitPoint A is the starting point A E B D C

  26. CircuitPoint A is the starting point A E B C D

  27. Simple Graphs

  28. Not, Simple Graphs

  29. Complete Graphs

  30. Complete Graphs Draw a complete graph with six nodes. Draw a complete graph with seven nodes

  31. Petroleum Delivers S N 490 370 570 325 T 825 M 565 520 565 745 380 C

  32. 1 Node

  33. 2 Nodes

  34. 2 Nodes

  35. 3 Nodes

  36. 3 Nodes

  37. 3 Nodes

  38. 3 Nodes

  39. 3 Nodes

  40. 3 Nodes

  41. 3 Nodes

  42. 3 Nodes 2 Routes

  43. 4 Nodes

  44. 4 Nodes

  45. 4 Nodes

  46. 4 Nodes

  47. 4 Nodes

  48. 4 Nodes

  49. 4 Nodes

  50. 4 Nodes

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