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Planar Graphs

Planar Graphs
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2013-06-24 10:58
PolygonGeometric ConstructionGraphing
In collections Graph theory
This example introduces the basic concepts of planar graphs. It constructs K_4, K_5, and K_{3,3} graphs to demonstrate their properties. The Segment command is used to draw edges, suitable for students at the middle school level and above.

GeoGebra Commands & Parameters

  1. Segment(K_4, B) → a
  2. Segment(B, C) → b
  3. Segment(C, D) → c
  4. Segment(D, K_4) → d
  5. Segment(K_4, C) → e
  6. Segment(B, D) → f
  7. Segment(K_5, E) → g
  8. Segment(E, F) → h
  9. Segment(F, G) → i
  10. Segment(G, H) → j
  11. Segment(H, K_5) → k
  12. Segment(K_5, F) → l
  13. Segment(E, H) → m
  14. Segment(K_5, G) → n
  15. Segment(G, E) → p
  16. Segment(F, H) → q
  17. Segment(K_{3,3}, I) → r
  18. Segment(I, J) → s
  19. Segment(K_{3,3}, K) → t
  20. Segment(K, L) → a_1
  21. Segment(L, M) → b_1
  22. Segment(M, J) → c_1
  23. Segment(J, K) → d_1
  24. Segment(K_{3,3}, M) → e_1
  25. Segment(L, I) → f_1
  26. Segment(A, N) → g_1
  27. Segment(N, O) → h_1
  28. Segment(O, P) → i_1
  29. Segment(P, Q) → j_1
  30. Segment(Q, R) → k_1
  31. Segment(R, S) → l_1
  32. Segment(S, T) → m_1
  33. Segment(T, U) → n_1
  34. Segment(U, A) → p_1
  35. Segment(A, V) → q_1
  36. Segment(V, N) → r_1
  37. Segment(V, O) → s_1
  38. Segment(V, P) → t_1
  39. Segment(V, Q) → a_2
  40. Segment(V, R) → b_2
  41. Segment(V, S) → c_2
  42. Segment(V, T) → d_2
  43. Segment(V, U) → e_2
  44. Segment(K_1, B_1) → a_3
  45. Segment(B_1, C_2) → b_3
  46. Segment(C_2, D_2) → c_3
  47. Segment(D_2, K_1) → d_3
  48. Segment(K_1, C_2) → e_3
  49. Segment(B_1, D_2) → f_3
  50. Segment(A_1, N_1) → g_2
  51. Segment(N_1, O_1) → h_2
  52. Segment(O_1, P_1) → i_2
  53. Segment(P_1, Q_1) → j_2
  54. Segment(Q_1, R_1) → k_2
  55. Segment(R_1, S_1) → l_2
  56. Segment(S_1, T_1) → m_2
  57. Segment(T_1, U_1) → n_2
  58. Segment(U_1, A_1) → p_2
  59. Segment(A_1, V_1) → q_2
  60. Segment(V_1, N_1) → r_2
  61. Segment(V_1, O_1) → s_2
  62. Segment(V_1, P_1) → t_2
  63. Segment(V_1, Q_1) → a_4
  64. Segment(V_1, R_1) → b_4
  65. Segment(V_1, S_1) → c_4
  66. Segment(V_1, T_1) → d_4
  67. Segment(V_1, U_1) → e_4

AI Drawing Prompt Reference

Draw a planar graph including K_4, K_5, and K_{3,3}. First, draw the four vertices A, B, C, D of K_4 and connect AB, BC, CD, DA, AC, BD. Then, draw the five vertices E, F, G, H, I of K_5 and connect EF, FG, GH, HI, IE, FG, GH, HI, IE. Finally, draw the six vertices J, K, L, M, N, O of K_{3,3} and connect JK, KL, LM, MJ, JK, LM, MN, JO, KO, LO, JO, KO, LO, MN.
The prompt above was compiled from the original drawing commands and is for reference only.