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Minimum Spanning Tree Generator and Calculator

Minimum Spanning Tree Generator and Calculator
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2017-02-14 04:20
OptimizationGeometric ConstructionGraphing
This example demonstrates the generation and calculation of Minimum Spanning Trees (MST) in graph theory, visually showing how to construct a tree connecting all vertices with the minimum total edge weight. Core mathematical concepts include graph theory, optimization, vertex connection, and edge weight comparison. It uses GeoGebra commands like Line, Point, Length, Segment, Intersect, LaTeX, and MinimumSpanningTree. Suitable for high school students and above learning graph algorithms, algorithm visualization, or as an introductory tool for computer science education.

GeoGebra Commands & Parameters

  1. Line(B_1, yAxis) → g
  2. Point(g) → D_1
  3. Line(D_1, xAxis) → i
  4. Point(i) → A_1
  5. Line(G_1, yAxis) → h
  6. Point(h) → C_1
  7. Length(Segment[D, G]) → dg_1
  8. Length(Segment[B, G]) → bg_1
  9. Length(Segment[B, D]) → bd_1
  10. Length(Segment[A, G]) → ag_1
  11. Length(Segment[A, B]) → ab_1
  12. Length(Segment[A, D]) → ad_1
  13. Length(Segment[B, C]) → bc_1
  14. Length(Segment[A, C]) → ac_1
  15. Length(Segment[C, G]) → cg_1
  16. Length(Segment[C, D]) → cd_1
  17. Length(Segment[D, E]) → de_1
  18. Length(Segment[C, E]) → ce_1
  19. Length(Segment[B, E]) → be_1
  20. Length(Segment[A, E]) → ae_1
  21. Length(Segment[E, G]) → eg_1
  22. Length(Segment[F, G]) → fg_1
  23. Length(Segment[D, F]) → df_1
  24. Length(Segment[B, F]) → bf_1
  25. Length(Segment[A, F]) → af_1
  26. Length(Segment[C, F]) → cf_1
  27. Length(Segment[E, F]) → ef_1
  28. Segment(A, B) → ab
  29. Line(A_1, yAxis) → f
  30. Line(B_1, xAxis) → j
  31. Intersect(j, f) → F_1
  32. Intersect(h, i) → H_1
  33. Segment(F_1, G_1) → k
  34. Segment(G_1, H_1) → l
  35. Segment(A_1, H_1) → m
  36. Segment(A_1, F_1) → n
  37. Segment(A, C) → ac
  38. Segment(B, C) → bc
  39. Segment(A, D) → ad
  40. Segment(B, D) → bd
  41. Segment(C, D) → cd
  42. LaTeX(matrix, true) → text1
  43. Segment(A, E) → ae
  44. Segment(A, F) → af
  45. Segment(B, E) → be
  46. Segment(B, F) → bf
  47. Segment(C, E) → ce
  48. Segment(C, F) → cf
  49. Segment(D, E) → de
  50. Segment(D, F) → df
  51. Segment(E, F) → ef
  52. Segment(A, G) → ag
  53. Segment(B, G) → bg
  54. Segment(C, G) → cg
  55. Segment(D, G) → dg
  56. Segment(E, G) → eg
  57. Segment(F, G) → fg
  58. MinimumSpanningTree({A, B, C, D, E, F, G}) → graph

AI Drawing Prompt Reference

Create a graph theory illustration for demonstrating minimum spanning tree algorithms. Start by setting up coordinate axes and placing several movable points on them. Connect these points with line segments to form multiple triangles and quadrilaterals, creating a weighted connected graph. The figure should include multiple vertices connected by segments, with each segment labeled by its length as the edge weight. The overall layout should clearly show the connections between vertices and emphasize the concept of a minimum spanning tree—connecting all vertices with minimal total edge weight. Include a coordinate grid for easy observation of point positions and distances.
The prompt above was compiled from the original drawing commands and is for reference only.