### Abstract

The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic -N? We answer this question for all N from -1 to 50, and we display a body of theorems and techniques which can be used to settle the question for more complicated surfaces. These include: two ways to diagram an action of symmetry group, an equivalence relation on vertices (rotation centers in general), several applications of Sylow theory, and some non-Sylow observations on the size of the symmetry group.

Original language | English (US) |
---|---|

Pages (from-to) | 241-274 |

Number of pages | 34 |

Journal | Discrete Mathematics |

Volume | 277 |

Issue number | 1-3 |

DOIs | |

State | Published - Feb 28 2004 |

### Fingerprint

### Keywords

- Graphs imbeddings
- Hypermaps
- Maps
- Non-orientable surfaces

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*277*(1-3), 241-274. https://doi.org/10.1016/j.disc.2003.03.001

**Surfaces having no regular hypermaps.** / Wilson, Stephen E; Breda D'Azevedo, Antonio.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 277, no. 1-3, pp. 241-274. https://doi.org/10.1016/j.disc.2003.03.001

}

TY - JOUR

T1 - Surfaces having no regular hypermaps

AU - Wilson, Stephen E

AU - Breda D'Azevedo, Antonio

PY - 2004/2/28

Y1 - 2004/2/28

N2 - The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic -N? We answer this question for all N from -1 to 50, and we display a body of theorems and techniques which can be used to settle the question for more complicated surfaces. These include: two ways to diagram an action of symmetry group, an equivalence relation on vertices (rotation centers in general), several applications of Sylow theory, and some non-Sylow observations on the size of the symmetry group.

AB - The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic -N? We answer this question for all N from -1 to 50, and we display a body of theorems and techniques which can be used to settle the question for more complicated surfaces. These include: two ways to diagram an action of symmetry group, an equivalence relation on vertices (rotation centers in general), several applications of Sylow theory, and some non-Sylow observations on the size of the symmetry group.

KW - Graphs imbeddings

KW - Hypermaps

KW - Maps

KW - Non-orientable surfaces

UR - http://www.scopus.com/inward/record.url?scp=0742302972&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0742302972&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2003.03.001

DO - 10.1016/j.disc.2003.03.001

M3 - Article

VL - 277

SP - 241

EP - 274

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -