mathematics Article The STEM Methodology and Graph Theory: Some Practical Examples Cristina Jordán 1,† , Marina Murillo-Arcila 2,† and Juan R. Torregrosa 1, * ,†   Citation: Jordán, C.; Murillo-Arcila, M.; Torregrosa, J.R. The STEM Methodology and Graph Theory: Some Practical Examples. Mathematics 2021, 9, 3110. https:// doi.org/10.3390/math9233110 Academic Editors: David Pugalee, Frank Werner, Michelle Stephan and Erdinç Çakıro ˘ glu Received: 11 October 2021 Accepted: 30 November 2021 Published: 2 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain; cjordan@mat.upv.es 2 Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain; mamuar1@upv.es * Correspondence: jrtorre@mat.upv.es † These authors contributed equally to this work. Abstract: In this paper, we highlight that Graph Theory is certainly well suited to an applications approach. One of the basic problems that this theory solves is finding the shortest path between two points. For this purpose, we propose two real-world problems aimed at STEM undergraduate students to be solved by using shortest path algorithms from Graph Theory after previous modeling. Keywords: weighted graphs; shortest path algorithms; Dijkstra; Bellman–Ford; modeling; STEM 1. Introduction The term STEM is the acronym for Science, Technology, Engineering, and Mathematics. The biggest advantage of STEM education is that it involves issues that affect students in their day-to-day lives, so focusing the lesson on real-world problems can motivate them. Furthermore, understanding the problem and learning the basic concepts can lead the students to innovate, which is a powerful skill for their future. Graph Theory has proven to be a powerful tool for modeling real-world problems, experiencing a boom in the last few decades due to its high applicability. The mathe- matical structures of Graph Theory are widely applied in several research areas such as biology [1,2], engineering [3,4], chemistry [5], economics [6], social networks [7], image processing [8], and education [9], among others. This shows that graphs provide an inter- disciplinary approach that builds connections between content and real-world context. In addition, given its intuitive graphical representation, basic concepts from Graph Theory could already be included in secondary school, since it is a relevant subject for providing the students awareness that studying mathematics is more than just applying methods. It also provides them with a set of tools to model problems, which we consider fundamental for the student due to its interdisciplinary applications. For these reasons, we believe that it is important to propose to the student problems whose modeling is not trivial. Despite the proven utility of Graph Theory in real-world applications, this subject, which is usually present in university studies of mathematics, computer science, and data science, is still taught without paying enough attention to modeling. Although, as we commented before, examples of direct applications of Graph Theory algorithms are proposed in the literature, it is not easy to find academic problems in a real context whose resolution is not limited to applying an algorithm to a graph, but rather, it is necessary to modify and adapt it in order to solve the problem. In relation to the methodology used in the teaching of graphs, educational innovations have been carried, out as can be found in the existing literature [10–12], although modeling does not appear frequently. In our opinion, this should be the main objective of teaching this subject. Thus, the methodology for which we advocate is based on starting the issues with the statement of a real context problem and, then, in view of the proposed issues, Mathematics 2021, 9, 3110. https://doi.org/10.3390/math9233110 https://www.mdpi.com/journal/mathematics