Abstract
A map, or a cellular division of a compact surface, is often viewed as a cellular imbedding of a connected graph in a compact surface. It generalises to a hypermap by replacing "graph" with "hypergraph". In this paper we classify the non-orientable regular maps and hypermaps with size a power of 2, the nonorientable regular maps and hypermaps with 1, 2, 3, 5 faces and give a sufficient and necessary condition for the existence of regular hypermaps with 4 faces on non-orientable surfaces. For maps we classify the non-orientable regular maps with a prime number of faces. These results can be useful in classifications of nonorientable regular hypermaps or in non-existence of regular hypermaps in some non-orientable surface such as in [5].
| Original language | English (US) |
|---|---|
| Pages (from-to) | 173-189 |
| Number of pages | 17 |
| Journal | Journal for Geometry and Graphics |
| Volume | 7 |
| Issue number | 2 |
| State | Published - Jan 1 2003 |
Keywords
- Graphs imbeddings
- Hypermaps
- Maps
- Non-orientable surfaces
ASJC Scopus subject areas
- Applied Psychology
- Geometry and Topology
- Applied Mathematics
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Wilson, S. E., & d'Azevedo, A. B. (2003). Non-orientable maps and hypermaps with few faces. Journal for Geometry and Graphics, 7(2), 173-189.