Investigating Graph Theory with GeoGebra

November 21, 2011 in Featured

Hall-Janko graph as Foster graph F + Steiner s...

Image via Wikipedia

GeoGebra is dynamic math software that can be used in the study of algebra, geometry, and calculus. It is free and can either be run inside a web browser, or downloaded and installed locally for offline use. I have been using GeoGebra with my algebra and geometry students for several years, but recently discovered its usefulness for my discrete math students as well. As a culminating project for our unit on graph theory, I ask students to create and name their own graph. We first look at the Gallery of Named Graphs to brainstorm ideas, and then I let them loose to create a unique graph of their own. They have to describe the characteristics of their graph, using the concepts we’ve studied throughout the unit such as:

  • is the graph planar?
  • is the graph bipartite?
  • is the graph a tree?
  • does that graph contain a Hamiltonian cycle?
  • what is the graph’s chromatic number?
  • is the graph isomorphic to any other well-known graphs?

Students then present their graphs to the class and ask the audience questions about its characteristics. Rather than simply drawing a picture of their graph on paper, students create their graphs in GeoGebra and export them as interactive web pages. This allows the presenter to manipulate the graph during the presentation. It also allows the presentation to be interactive. Volunteers can come forward and try to show that the graph is planar, for example.

Here is a sample student project: The Hippo Snark
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