Abstract: The novel topology of the molecular cylinder and MÖbius strip with three-rung and four-rung ladder is discussed. Some novel results in the low dimensional topology deriving from consideration of topological symmetry of the molecular graphs defined by the subject compounds are also discussed. The Hiickel-type molecules with the even number of twists and the MÖbius-type molecule with the odd number of twists are defined. It is shown that for the Hiickel-type and MÖbius-type molecules with vertices and edges of constitutionally equivalent or nonequiva-lent, the topological symmetry is topological invarants(homeomorphic), while Tof the number of twist are not isotopic variable. The topological chirality of these molecules, which is an interesting problem, has been solved with the invention of the topological symmetry concept applied to molecular structures. In order to completely characterize a molecule it is useful to understand the symmetries of its molecular graph in₃-space. For this purpose the topological equivalent graph and topological symmetry are said to be rigid.

Key words: Topological stereochemistry, Topological stereoisomer, Topological chirality