Regular self-dual and self-Petrie-dual maps of arbitrary valency

Jay Fraser, Olivia Jeans, Jozef Širáň

Abstract


The existence of a regular, self-dual and self-Petrie-dual map of any given even valency has been proved by D. Archdeacon, M. Conder and J. Širáň (2014). In this paper we extend this result to any odd valency ≥ 5. This is done using algebraic number theory and maps defined on the groups PSL(2, p) in the case of odd prime valency ≥ 5 and valency 9, and using coverings for the remaining odd valencies.


Keywords


Regular map, automorphism group, self-dual map, self-Petrie-dual map

Full Text:

PDF ABSTRACTS (EN/SI)


DOI: https://doi.org/10.26493/1855-3974.1749.84e

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications