Regular self-dual and self-Petrie-dual maps of arbitrary valency
Combinatorics
2018-08-01 v1
Abstract
The main result of D. Archdeacon, M. Conder and J. \v{S}ir\'a\v{n} [Trans. Amer. Math. Soc. 366 (2014) 8, 4491-4512] implies existence of a regular, self-dual and self-Petrie dual map of any given even valency. In this paper we extend this result to any odd valency . This is done by algebraic number theory and maps defined on the groups in the case of odd prime valency and valency , and by coverings for the remaining odd valencies.
Keywords
Cite
@article{arxiv.1807.11692,
title = {Regular self-dual and self-Petrie-dual maps of arbitrary valency},
author = {Jay Fraser and Olivia Jeans and Jozef Širáň},
journal= {arXiv preprint arXiv:1807.11692},
year = {2018}
}