Exploration of regularities in bipartite graphs using GEOGEBRA software

Abstract

A classroom proposal is presented to integrate contents of Graph Theory and Linear Algebra in complete bipartite graphs, linking adjacency and Laplacian matrices, the eigenvalues of graphs will be determined, applicable to connectivity concepts. Students will be given exploration activities working with GeoGebra software, starting from several particular cases, with table works and questionnaires to be completed, in order to determine patterns on the eigenvalues of adjacency and Laplacian matrices of complete bipartite graphs. The work with patterns will lead to the generalization process, to abstract properties from observation and experimentation on examples. This learning experience builds bridges between the concrete and the symbolic, and the student is initiated in research