Prom a mathematical point of view, in 1988 F. Zhang, X. Guo and R. Chen introduced "Z-transformation graph" (Randic named after "resonance graph" in chemical literature) of perfect matchings of hexagonal systems: from a perfect matching to another is joined by an edge provided they only differ in a hexagon. Afterwards, this concept was extended naturally to general plane bipartite graphs. Its nature can be explained in many ways from chemical resonance to mathematical cycle space and distributive lattice. We now survey rich theoretical results on this field made by several groups in main directions: chemical application, basic properties, connectivity, forcing edge, lattice structure, distance and median graphs, coding, as well as some miscellaneous problems.
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