Counting unlabelled toroidal graphs with no K33-subdivisions
  We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of core graphs. Using structure theorems for toroidal and projective-planar graphs containing no K33-subdivisions, we apply these techniques to obtain their unlabelled enumeration. 
Andrei Gagarin, Gilbert Labelle, Pierre Leroux (LaCIM, Universite du   Quebec a Montreal)