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 |
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Keywords
- Graphs imbeddings
- Hypermaps
- Maps
- Non-orientable surfaces
ASJC Scopus subject areas
- Applied Psychology
- Geometry and Topology
- Applied Mathematics
Cite this
Non-orientable maps and hypermaps with few faces. / Wilson, Stephen E; d'Azevedo, Antonio Breda.
In: Journal for Geometry and Graphics, Vol. 7, No. 2, 01.01.2003, p. 173-189.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Non-orientable maps and hypermaps with few faces
AU - Wilson, Stephen E
AU - d'Azevedo, Antonio Breda
PY - 2003/1/1
Y1 - 2003/1/1
N2 - 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].
AB - 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].
KW - Graphs imbeddings
KW - Hypermaps
KW - Maps
KW - Non-orientable surfaces
UR - http://www.scopus.com/inward/record.url?scp=85011638728&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85011638728&partnerID=8YFLogxK
M3 - Article
VL - 7
SP - 173
EP - 189
JO - Journal for Geometry and Graphics
JF - Journal for Geometry and Graphics
SN - 1433-8157
IS - 2
ER -