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Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs |
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| Authors: | M.J. Grannell |
| Affiliation: | a Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom b National University of Chernivtsi, Chernivtsi, Ukraine c Institute of Applied Problems of Mechanics and Mathematics of National Academy of Science of Ukraine, Lviv, Ukraine |
| Abstract: | We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n+1 rungs. Such an assignment yields an index one current graph with current group Z12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our characterization to construct Skolem sequences that give rise to such current assignments. These produce many nonisomorphic orientable biembeddings of cyclic Steiner triple systems of order 12n+7. |
| Keywords: | Topological embedding Complete graph Skolem sequence Steiner triple system |
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