The Auslander curve, introduced by Burban-Drozd(2011), is a certain non-commutative sheaf on a projective curve. Its derived category, in some cases, admits a tilting complex. Lekili-Polishchuk(2018) extended this idea to nodal stacky curves, and showed that the derived category of the Auslander curve in this setting is equivalent to the partially wrapped Fukaya category of some graded marked surfaces. This establishes a version of homological mirror symmetry in those cases. Burban-Drozd(2019) further generalized the construction to a broader class of nodal curves. We discuss the graded marked surfaces corresponding to these curves under the homological mirror symmetry.