P37: Enumeration of all connected bipartite permutation graphs with $n$ vertices

P37: Enumeration of all connected bipartite permutation graphs with $n$ vertices
Input:
A graph size $n$.
Output:
All connected bipartite permutation graphs.
Complexity:
$O(1)$ time per graph with $O(n)$ space.
Comment:
Reference:
[Saitoh2010b] (Bibtex)