Triangular embeddings of complete graphs (neighborly maps) with 12 and 13 vertices
✍ Scribed by M. N. Ellingham; Chris Stephens
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 133 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1063-8539
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✦ Synopsis
In this paper, we describe the generation of all nonorientable triangular embeddings of the complete graphs K 12 and K 13 . (The 59 nonisomorphic orientable triangular embeddings of K 12 were found in 1996 by Altshuler, Bokowski, and Schuchert, and K 13 has no orientable triangular embeddings.) There are 182; 200 nonisomorphic nonorientable triangular embeddings for K 12 , and 243, 088, 286 for K 13 . Triangular embeddings of complete graphs are also known as neighborly maps and are a type of twofold triple system. We also use methods of Wilson to provide an upper bound on the number of simple twofold triple systems of order n, and thereby on the number of triangular embeddings of K n . We mention an application of our results to flexibility of embedded graphs.