Graph Theory for Kids

Šárka Voráčová, leucotea, Aug 11, 2017

We wanted to explore some elementary ideas in graph theory, which we view as mathematically rich, yet accessible to children. GeoGebra book is inpired by Joel David Hamkins articles on graph theory for seven and eight olds. [url]http://jdh.hamkins.org/math-for-seven-year-olds-graph-coloring-chromatic-numbers-eulerian-paths/[/url]


  • 1. Planar graph of regular hexahedron
  • 2. Planar graph of regular octahedron
  • 3. Planar graph of a dodecahedron
  • 4. The smallest four-colouring mosaic
  • 5. Four color challenge
  • 6. Dodecahedron coloring
  • 7. Vertex coloring
  • 8. Four colour theorem
  • 9. Petersen Graph
  • 10. Cat Maze
  • 11. Turtle in the labyrinth
  • 12. Eulerian Path by Turtle
  • 13. Simple Eulerian graphs
  • 14. Euler Circuit
  • 15. Minimum Spanning Tree Demonstration
  • 16. Miami University Campus Traveling Salesman Problem
  • 17. The Shortest Path in the Graph
  • 18. Aplicació Dijkstra
  • 19. Travelling salesman
  • 20. Voronoi Diagram Animation

1.

Planar graph of regular hexahedron

Move the gray vertices of the hexahedron on the left picture to get planar graph on the right.
[url=https://en.wikipedia.org/wiki/Planar_graph]Planar graph[/url] ([url=https://en.wikipedia.org/wiki/Schlegel_diagram]Schlegel diagram[/url]) of a convex polyhedra lack scale, distance and shape, but the relationship between points is maintained.[br] [b]Euler's formula[/b] states that if a finite, [url=https://en.wikipedia.org/wiki/Connectivity_%28graph_theory%29]connected[/url], planar graph is drawn in the plane without any edge intersections, and [i]v[/i] is the number of vertices, [i]e[/i] is the number of edges and [i]f[/i] is the number of faces (regions bounded by edges, including the outer, infinitely large region), then [i]v - e + f = 2[/i]. Thanks to Schlegel diagram it is clear that Euler's formula is also valid for [url=https://en.wikipedia.org/wiki/Convex_polyhedron]convex polyhedra[/url].
The skeleton of [url=https://en.wikipedia.org/wiki/Hexahedron]hexahedron[/url] (the vertices and edges) form a graph. It is one of 5 [url=http://mathworld.wolfram.com/PlatonicGraph.html]Platonic graphs[/url], each a skeleton of its [url=https://en.wikipedia.org/wiki/Platonic_solid] Platonic solid[/url].
– Šárka Voráčová

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