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Nonplanar Graphs

Nonplanar Graphs
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2013-06-28 13:18
FunctionGeometric ConstructionGraphing
In collections Graph theory
This example demonstrates the concept of nonplanar graphs by transforming K_6 to reveal subgraphs K_{3,3} and K_5. Key math concepts include planarity in graph theory, Kuratowski's theorem, and minor graphs. Construction involves commands like Segment, and objects such as text1_1, text2_1, K11_2, K13_2, etc., to draw and annotate the graphs, with r_3, K_7, and others aiding transformations. Suitable for high school and above, focusing on graph theory fundamentals and complex graph analysis.

GeoGebra Commands & Parameters

  1. Segment(K11_2, K14_2) → r_3
  2. Segment(K13_2, K_7) → t_3
  3. Segment(K14_2, K13_2) → f_2
  4. Segment(K11_2, K_7) → g_2
  5. Segment(K_4, K14_2) → a
  6. Segment(K_4, K_7) → b
  7. Segment(K_3, K13_2) → c
  8. Segment(K_3, K11_2) → d
  9. Segment(K_4, K_3) → f
  10. Segment(K_1, K_2) → e
  11. Segment(K_2, K_6) → g
  12. Segment(K, K_5) → h
  13. Segment(K_5, K_6) → i
  14. Segment(K, K_1) → j
  15. Segment(K_1, K_6) → k
  16. Segment(K_5, K_2) → l
  17. Segment(K, K_6) → m
  18. Segment(K_2, K) → n
  19. Segment(K_5, K_1) → p
  20. Segment(A_{0}, A_{1}) → a_{0}
  21. Segment(A_{1}, A_{2}) → a_{1}
  22. Segment(A_{2}, A_{3}) → a_{2}
  23. Segment(A_{0}, A_{4}) → a_{3}
  24. Segment(A_{4}, A_{5}) → a_{4}
  25. Segment(A_{5}, A_{3}) → a_{5}
  26. Segment(A_{4}, A_{2}) → a_{6}
  27. Segment(A_{1}, A_{5}) → a_{7}
  28. Segment(A_{3}, A_{0}) → a_{8}
  29. Segment(A_{1}, A_{3}) → a_{9}
  30. Segment(A_{0}, A_{5}) → a_{10}
  31. Segment(A_{3}, A_{4}) → a_{11}
  32. Segment(A_{5}, A_{2}) → a_{12}
  33. Segment(A_{4}, A_{1}) → a_{13}
  34. Segment(A_{2}, A_{0}) → a_{14}