see also Kauer-Roggenkamp for general form of mutations of graph orders, as well as Gnedin for Calabi-Yau properties. This relates to the construction of a AQFT related to Artin L-functions and dessins d’enfants. This is related to Seiberg duality in type IIB string theory derived from quiver gauge theories. See also https://arxiv.org/abs/0803.1328 for combinatorial constructions.
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