A classification of prime-valent regular Cayley maps on some groups
Combinatorics
2010-11-01 v1
Abstract
A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are balanced and all prime-valent regular Cayley maps on abelian groups are either balanced or anti-balanced. Furthermore, we prove that there is no prime-valent regular Cayley map on any dicyclic group.
Keywords
Cite
@article{arxiv.0709.2217,
title = {A classification of prime-valent regular Cayley maps on some groups},
author = {Dongseok Kim and Young Soo Kwon and Jaeun Lee},
journal= {arXiv preprint arXiv:0709.2217},
year = {2010}
}