Non-orientable maps and hypermaps with few faces

Stephen E Wilson, Antonio Breda d'Azevedo

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)173-189
Number of pages17
JournalJournal for Geometry and Graphics
Volume7
Issue number2
StatePublished - Jan 1 2003

Fingerprint

Regular Map
Non-orientable Surface
Face
Classify
Imbedding
Prime number
Hypergraph
Nonexistence
Connected graph
Division
Necessary Conditions
Generalise
Sufficient Conditions
Graph in graph theory

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 journalArticle

Wilson, Stephen E ; d'Azevedo, Antonio Breda. / Non-orientable maps and hypermaps with few faces. In: Journal for Geometry and Graphics. 2003 ; Vol. 7, No. 2. pp. 173-189.
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