A classification of prime-valent regular Cayley maps on some groups

Details A classification of prime-valent regular Cayley maps on some groups A classification of prime-valent regular Cayley maps on some groups

2007-09-14

arxiv.org/abs/0709.2217v1

Bull. Korean Math. Soc. 47 (2010) 17-27

Mathematics

Combinatorics

Scientific paper

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.

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