The connectivity of Z-transformation graphs of perfect matchings of polyominoes Original Research Article

A polyomino, or any shaped chessboard, consists of finite cells of a plane square grid as its connected subgraph such that each interior face is surrounded by a cell. The Z-transformation graph Z(G) of a polyomino G is a graph in which the vertices are the perfect matchings of G and two vertices are adjacent provided that the union of the corresponding two perfect matchings of G contain exactly one cycle and the cycle consists of the four edges of a cell. This paper presents some properties of polyominoes with perfect matchings and mainly shows that the connectivity of Z(G) reaches its minimum degree with only two exceptions.