Regular maps on non-orientable surfaces
type: Item
instance of: scholarly article
title: Regular maps on non-orientable surfaces
zbMATH Open document ID: 0832.05053
DOI: 10.1007/BF01267644
author: Brent Everitt
author: Marston D. E. Conder
published in: Geometriae Dedicata
publication date: 1996-02-20T00:00:00Z
review text: A map on a non-orientable surface is a 2-cell imbedding of a connected graph into the surface; the map is regular if its automorphism group has the largest possible order: four times the number of edges of the graph. It is well-known (see, for example, \textit{H. S. M. Coxeter} and \textit{W. O. J. Moser}, Generators and relations for discrete groups, 4th edition, Springer-Verlag, Berlin (1980; Zbl 0422.20001)) that there are regular maps on the projective plane \(N_1\) (the two-fold covering projection of the dodecahedron imbeds the Petersen graph regularly on the projective plane, for example), but there are no regular maps either on the Klein bottle \(N_2\) or on \(N_3\). The present authors construct several infinite families of regular maps, to show that such maps exist on non- orientable surfaces of more than 77\% of all possible genera.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 806257
zbMATH Keywords: map
zbMATH Keywords: non-orientable surface
zbMATH Keywords: imbedding
zbMATH Keywords: automorphism group
zbMATH Keywords: regular maps
zbMATH Keywords: projective plane
zbMATH Keywords: Klein bottle
reviewed by: Arthur T. White
describes a project that uses: Cayley
MaRDI profile type: Publication
cites work: Q3050438
cites work: Q3333220
cites work: The Abstract Groups G m,n,p
cites work: Q3855356
cites work: Operators over regular maps
cites work: Cantankerous maps and rotary embeddings of \(K_ n\)
full work available at URL: https://doi.org/10.1007/bf01267644
OpenAlex ID: W2031900816
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description: scientific article; zbMATH DE number 806257