Z-transformation graphs of perfect matchings of hexagonal systems (Q1825211)

Given a hexagonal system H, the Z-transformation graph Z(H) is the graph whose vertices are perfect matchings of H. Two vertices are adjacent in Z(H) if the symmetric difference of the corresponding matchings is a hexagon of H. The authors give some properties of this transformation graph: Z(H) is bipartite, connected and is either a path or a graph of girth 4. In addition, they characterize those hexagonal systems whose Z- transformation graphs are not 2-connected.