<![CDATA[This research aims to investigate the impact of the discrete mathematics lecture process on deductive reasoning abilities, especially in carrying out proofs in graph theory. This research uses qualitative research based on the results of observations of the learning process in the Discrete Mathematics course. The subjects of this research were three students from the Mathematics Education Study Program who were pre-service teachers and in-service mathematics teachers at a university in Malang. The data collection technique is a description and observation test question sheet. The research results show that the process of learning graph theory in discrete courses is through explanations related to the definition of graph coloring, examples of the application of theorems, practice questions through guided proof with lecturers, and the application of graph coloring theory in everyday life. Overall, the graph theory learning process emphasizes deductive reasoning abilities. Based on the results of the analysis of the four-color theorem test, in general, it succeeded in having a good impact on students in the mathematics education study program.]]>
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