Cubic leaves of partial triple systems

A leave of a partial triple system (V,B) is a graph (V,E) in which E in the set of unordered pairs not appearing in any triple of B.

There are 21 pairwise nonisomorphic cubic graphs of order 10. Seven of them are cubic leaves, admitting together 20 partial triple systems.
For order 12, there exist 94 pairwise nonisomorphic cubic graphs; 76 of them are cubic leaves, admitting together 3172 partial triple systems.

Downloadable files:
cl_10.txt [3K]
cl_12.txt [501K]
cl_12.zip [40K]