This paper addresses the concepts of Graph Theory and its potential for teaching in Basic
Education, using mathematical modeling as a methodology that promotes meaningful learning.
It explores the New High School and the organization of formative itineraries, which provide
opportunities to delve deeper into the subject with students. Graph Theory is introduced theo-
retically, with definitions, concepts, representation, history, and main theorems. The Pagerank
Algorithm is explained in a simplified manner to promote the integration of theory with the
use of graphs in everyday life, which many people use but are unaware of. Finally, activities
are proposed that aim to introduce Graph Theory as a method for problem-solving. The central
objectives include understanding the role of mathematics as a science that investigates patterns
and applying mathematical modeling through graphs to solve problems. It is concluded that the
development of investigative activities related to the topic can improve the understanding of
mathematical concepts from other areas and promote the development of analytical and orga-
nizational skills and competencies related to the Brazilian National Common Curricular Base.
The methodology used was bibliographic and exploratory, with the purpose of exploring in the
literature the foundations of Graph Theory, as well as its possible approaches in the classroom,
targeting mathematics teachers.
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