For 3-connected G, G □ H embeds on the torus iff G is outer-cylindrical and H = P₂; additionally K₄ □ P₃ has genus two.
109, 1992, Algebraic graph theory (Leibnitz, 1989), pp
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Toroidal Cartesian Products Where One Factor is 3-Connected
For 3-connected G, G □ H embeds on the torus iff G is outer-cylindrical and H = P₂; additionally K₄ □ P₃ has genus two.