P147: Enumeration of all maximal planar graphs with $n$ vertices

P147: Enumeration of all maximal planar graphs with $n$ vertices
Input:
An integer $n$.
Output:
All maximal planar graph with $n$ vertices.
Complexity:
$O(n^3)$ time per graph with $O(n)$ space.
Comment:
A planar graph with $n$ vertices is \textit{maximal} if it has exactly $3n -6$ edges.
Reference:
[Nakano2004a] (Bibtex)