After the fullerenes have been found, it is a natural question to ask whether there are torus-shaped 《graphitoid》 carbon molecules which may be called toroidal graphitoids. Note that the torus is the only closed surface S that can carry graphs G such that all vetices of G have degree 3 and all faces of the embedding of G in S are hexagons (Finure 1). In what follows, such (hypothetical) mole- cules (see Ref. la) and their molecular graphs will be referred to as 《torenes》. Note that the first paper about this topic was given by M. Randic, Y. Tsukano, and H. Hosoya.
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