This paper focuses on vertex-edge and graph topics in Prekindergarten to Grade 2, including an overview of the design level of the question and student's strategy in solving problems related to the topic. It discusses how the topic should be introduced in Prekindergarten to Grade 2 and the efforts to facilitate and support the level-question adoption of vertex-edge and graph topics for those graders. Fourteen students participated in this study from different schools in South Sumatra, Indonesia. This research was a development study using design research implementation with quantitative data analysis by testing, and qualitative by face-to-face interview. The results showed that students assessed a question categorized into easy, medium, and hard levels according to the questions' complexity. This study can be used as a guidance to teach vertex-edge and graph topics more interestingly.
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