Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs
نویسندگان
چکیده
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. Running head: Orientable biembeddings Corresponding author: V. P. Korzhik, Bogomoltsa St. 3/5, Chernivtsi, 58001, Ukraine. Email: [email protected] AMS classifications: 05B07, 05C10.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 309 شماره
صفحات -
تاریخ انتشار 2009