Z-transformation graph

[math]\displaystyle{ Z }[/math]-transformation graph --- [math]\displaystyle{ Z }[/math]-преобразованный граф.

[math]\displaystyle{ Z }[/math]-transformation graph, [math]\displaystyle{ Z_{F}(G) }[/math], of [math]\displaystyle{ G }[/math] with respect to a specific set [math]\displaystyle{ F }[/math] of faces is a graph on the perfect matchings of [math]\displaystyle{ G }[/math], such that two perfect matchings [math]\displaystyle{ M_{1} }[/math] and [math]\displaystyle{ M_{2} }[/math] are adjacent provided [math]\displaystyle{ M_{1} }[/math] and [math]\displaystyle{ M_{2} }[/math] differ only in a cycle that is the boundary of a face in [math]\displaystyle{ F }[/math]. If [math]\displaystyle{ F }[/math] is a set of all interior faces, [math]\displaystyle{ Z_{F}(G) }[/math] is a usual [math]\displaystyle{ Z }[/math]-transformation graph; if [math]\displaystyle{ F }[/math] contains all faces of [math]\displaystyle{ G }[/math] it is a novel graph called the total [math]\displaystyle{ Z }[/math]-transformation graph.