<![CDATA[This study aims to analyze university students’ visual representation errors in understanding the concepts of planar graphs, duality, and embedding. The investigation focuses on identifying error types, characterizing students’ thinking processes, and determining the factors contributing to these misconceptions. A descriptive qualitative approach was employed with two students selected as participants based on diagnostic test results and purposive sampling considerations. Data were collected through a visual representation test and task-based interviews. The findings reveal three main categories of errors: (1) inaccuracies in identifying vertices, edges, and faces; (2) errors in redrawing embeddings that fail to preserve the graph’s structure, resulting in violations of planarity; and (3) misconceptions regarding duality relationships between faces. Contributing factors include limited visual–spatial ability, insufficient foundational understanding of graph theory, and a lack of experience in manipulating complex graphs. These findings highlight the need to strengthen visual-based instruction, provide structured representational practice, and incorporate digital tools to support learning in graph theory.]]>
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