Ressaltando o aspecto interdisciplinar da Matemática para o Ensino Médio: uma abordagem algébrica na solução de problemas sobre grafos

Abstract

In this present work, motivated to emphasize the interdisciplinary character of mathematics to an high school level student, the relation between graphs, an important topic in combinatorics, and groups, an essential structure in algebra study, is explored while applied to some problem resolution . The concepts and properties are settled from formulation of tangible problems and accessible language to the target audience. The importance of graphs and groups concepts, connected in this work, justify and stress the use of such relations. The concept of a graph and related properties are formulated from the graphic representation of some problems. The group concept is introduced from the observation of the properties of mathematical objects studied all over the years at school. Finally, at the end, the connection between graphs and algebra is made by the study of an automorphism group of a graph. This connection is used to solve counting problems and a geometry problem.