Total Z-transformation graphs of perfect matching of plane bipartite graphs

The total Z-transformation graph and digraph of perfect matchings of a plane bipartite graph are defined. For a plane elementary bipartite graph it is shown that its total Z-transformation graph and digraph are 2-connected and strongly connected respectively. As an immediate consequence, we have that a plane bipartite graph is elementary if and only if its total Z-transformation digraph is strongly connected.