Given a periodic graph, we wish to determine via combinatorial methods whether it has periodic embeddings in the plane that—via motions that preserve edge-lengths and periodicity—can be continuously deformed into another non-congruent embedding of the graph. By introducing NBAC-colourings for the corresponding quotient gain graphs, we identify which periodic graphs have flexible embeddings in the plane when the lattice of periodicity is fixed. We further characterise with NBAC-colourings which 1-periodic graphs have flexible embeddings in the plane with a flexible lattice of periodicity, and characterise in special cases which 2-periodic graphs have flexible embeddings in the plane with a flexible lattice of periodicity.

给定一个周期图，我们希望通过组合方法确定它是否在平面中具有周期性嵌入——通过保持边长和周期性的运动——可以连续变形为图的另一个非全等嵌入。通过为相应的商增益图引入 NBAC 着色，我们确定了当周期性晶格固定时哪些周期性图在平面中具有灵活的嵌入。我们进一步用 NBAC 着色来表征 1-周期图在平面中具有灵活的周期性点阵的灵活嵌入，并在特殊情况下表征 2-周期图在具有灵活周期性点阵的平面中具有灵活的嵌入。