The present research consists of proposing methodologies that aim to work on graph theory making use of problematic methods and heuristic principles of teaching-learning of Mathematics. It aims to develop a methodological proposal that contributes to the improvement of the teaching-learning process of Graph Theory and its applications in Higher Education, that is, in ISPCAB, based on the mental schemes presented by Biembengut and Hein. SPSS and R-Studio statistical software were used to extrapolate data obtained from the questionnaire applied to teachers and students and the pre-test and post-test that were applied to 55 students; An analytical approach was made to the theoretical foundations of the object of study, with an emphasis on teaching methods (which are the teacher's actions to organize teaching activities in order to promote student learning). This was followed by the characterization of the current state, where difficulties of various types were found, such as the lack of a clear, deep and objective introduction of the concepts related to the different types of graphs; difficulties in extracting the matrix, both adjacency and incidence, in a graph and difficulties in interpreting problems involving graph theory, by the way they are formulated. Then, we elaborate, present, indicate proposals and propose methodologies to be adopted to minimize, if not, overcome these difficulties through problematic teaching.
