Intrinsic Properties of Spatial Graphs - Denison University

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$Math 232 syllabus - Denison University$

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Introduction Linking and Knotting Other Intrinsic Properties ConclusionTopological Symmetry GroupsThe topological symmetry group was introduced by Jon Simonin 1986 to study the symmetries of molecules whose structureis not rigid. It can be used to study the symmetries of any graphembedded in S 3 .DefinitionLet γ be an abstract graph with automorphism group Aut(γ).Let Γ be an embedding of γ in S 3 . The (orientation preserving)topological symmetry group of Γ, denoted TSG + (Γ), is thesubgroup of Aut(γ) induced by orientation preservinghomeomorphisms of the pair (S 3 , Γ).Blake MellorIntrinsic Properties of Spatial Graphs
Introduction Linking and Knotting Other Intrinsic Properties ConclusionTopological Symmetry GroupsThe topological symmetry groups of complete graphs havebeen completely classified (Flapan, M, Naimi, 2012). Forexample:Theorem (Flapan, M, Naimi, 2012)A complete graph K m with m ≥ 4 has an embedding Γ in S 3such that TSG + (Γ) = S 4 if and only if m ≡ 0, 4, 8, 12, 20(mod 24).Blake MellorIntrinsic Properties of Spatial Graphs
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