Topological Symmetry Groups of Complete Bipartite Graphs
| Autor: | Matthew Pittluck, Kathleen Hake, Blake Mellor |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
General Mathematics
010102 general mathematics Geometric Topology (math.GT) Symmetry group Topology 01 natural sciences Graph 010101 applied mathematics Mathematics - Geometric Topology 57M25 Homogeneous space FOS: Mathematics Bipartite graph Mathematics - Combinatorics Embedding Combinatorics (math.CO) 0101 mathematics 57M25 05C10 05C10 Mathematics |
| Zdroj: | Tokyo J. of Math. 39, no. 1 (2016), 133-156 |
| ISSN: | 0387-3870 |
| DOI: | 10.3836/tjm/1459367261 |
| Popis: | The symmetries of complex molecular structures can be modeled by the {\em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular abstract graphs. This question has been answered for complete graphs; it is natural next to consider complete bipartite graphs. In previous work we classified the complete bipartite graphs that can realize topological symmetry groups isomorphic to $A_4$, $S_4$ or $A_5$; in this paper we determine which complete bipartite graphs have an embedding in $S^3$ whose topological symmetry group is isomorphic to $\mathbb{Z}_m$, $D_m$, $\mathbb{Z}_r \times \mathbb{Z}_s$ or $(\mathbb{Z}_r \times \mathbb{Z}_s) \ltimes \mathbb{Z}_2$. Comment: 26 pages, minor revisions; this is the final version accepted by Tokyo Journal of Mathematics |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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