Richter, Bruce R.; Siran, Jozef and Wang, Yan
(2012).
Self-dual and self-Petrie-dual regular maps.
Journal of Graph Theory, 69(2) pp. 152–159.
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Abstract
Regular maps are cellular decompositions of surfaces with the “highest level of symmetry”, not necessarily orientation-preserving. Such maps can be identified with three-generator presentations of groups G of the form G=‹a,b,c|a2 =b2=c2=(ab)k =(bc)m=(ca)2 =•••=1›; the positive integers k and m are the face length and the vertex degree of the map. A regular map (G;a,b,c) is self-dual if the assignment b|→b,c |→a and a |→c extends to an automorphism of G, and self-Petrie-dual if G admits an automorphism fixing b and c and interchanging a with ca. In this note we show that for infinitely many numbers k there exist finite, self-dual and self-Petrie-dual regular maps of vertex degree and face length equal to k. We also prove that no such map with odd vertex degree is a normal Cayley map.
| Item Type: |
Journal Article
|
| Copyright Holders: |
2011 Wiley Periodicals, Inc |
| ISSN: |
0364-9024 |
| External Project Funding Details: |
| Funded Project Name | Project ID | Funding Body |
|---|
| Not Set | Not Set | NSERC | | Not Set | Not Set | VEGA Research Grant [1/0489/08] | | Not Set | Not Set | APVV Research Grant [0040-06 and 0104-07] | | Not Set | Not Set | APVV LPP Research Grant [0145-06 and 0203-06] |
|
| Keywords: |
regular map; triangle group; self-dual map; self-Petrie-dual map |
| Academic Unit/Department: |
Mathematics, Computing and Technology
Mathematics, Computing and Technology > Mathematics and Statistics |
| Item ID: |
32160 |
| Depositing User: |
Jozef Siran
|
| Date Deposited: |
03 Feb 2012 11:54 |
| Last Modified: |
30 Nov 2012 10:40 |
| URI: |
http://oro.open.ac.uk/id/eprint/32160 |
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