In the most general sense, mathematical thinking can be defined as using mathematical techniques, concepts, and methods, directly or indirectly, in the problem-solving process. In this study, efforts were made to include the Graph Theory of mathematics, which is found abundantly in physics, chemistry, computer networks, economics, administrative science, data communication, transportation planning, engineering, and similar areas of daily life, into the mathematics instruction process. Because suitable problems are selected in graph theory, the mathematical thinking skills of the students can be developed. A fundamental, qualitative research approach was adopted in this study, in which the mathematical thinking processes of 12th-grade students were examined. Two girls and two boys with average and high mathematics success who were in the 12th grade of a public school in Balikesir in the 2018-2019 Academic School year constituted the working group of the research. The data in the study were collected with the two worksheets the researchers prepared, the clinical interviews held during the application, and through unstructured observations. The results obtained by analyzing the data in the process of mathematics teaching, in which graph theory included are: When students solved the problems they faced and when they ascend top steps of mathematical thinking, they showed a better performance when compared to the other studies. Because, in the steps of privatization, generalization and assumption, only 1 of the total 8 responses given by the students is empty. At the stage of proof which is the final stage of mathematical thinking, the students have achieved a success rate of 75% despite they did not have a lesson about making proofs. This situation was interpreted as the visual model of problems selected from graph theory and attracting the attention of the questions as stated by the students. The results of this study show that, in the process of mathematics teaching, especially if teachers provide enough diversity students by using different fields of mathematics, they can increase the performances of students in mathematical thinking stages.