APR Tilting Modules and Graded Quivers with Potential

We study quivers with relations of endomorphism algebras of Auslander-Platzeck-Reiten tilting modules. It is known that the quivers are given by reflections if the original algebras have global dimension 1. We generalize this result for algebras with global dimension 2. In particular, we give an explicit description of the quivers with relations by mutations of quivers with potential (QPs). This result also provides a rich source of derived equivalence classes of algebras in a combinatorial way. As an application, we give a sufficient condition of QPs such that Derksen–Weyman–Zelevinsky's question [7, Question 12.2] has a positive answer.