Abstract.
Face 2-colourable triangular embeddings of complete tripartite graphs
Kn,n,n correspond to biembeddings of Latin squares of side
n.
We consider biembeddings that contain any of the five Latin squares derived
from the Cayley tables of finite groups of order 8.
Up to isomorphism, we determined all such biembeddings.
As regards their number:
-
the Cayley table of cyclic group C8 is in 701
nonisomorphic biembeddings;
-
the Cayley table of C4xC2 is in 1,964
nonisomorphic biembeddings;
-
the Cayley table of C2xC2xC2 is in
49 nonisomorphic biembeddings;
-
the Cayley table of dihedral gropup D4 is in 227
nonisomorphic biembeddings;
-
the Cayley table of quaternion gropup Q is in 236
nonisomorphic biembeddings