Regular Cayley maps for finite abelian groups

Regular Cayley maps for finite abelian groups

A regular Cayley map for a finite group A is an orientable map whose orientation-preserving automorphism group G acts regularly on the directed edge set and has a subgroup isomorphic to A that acts regularly on the vertex set. This paper considers the problem of determining which abelian groups have regular Cayley maps. The analysis is purely algebraic, involving the structure of the canonical ...

Regular Cayley maps for nite abelian groups

Reflexibility of regular Cayley maps for abelian groups

In this paper, properties of reflexible Cayley maps for abelian groups are investigated, and as a result, it is shown that a regular Cayley map of valency greater than 2 for a cyclic group is reflexible if and only if it is anti-balanced.

A Classification of Prime-valent Regular Cayley Maps on Abelian, Dihedral and Dicyclic Groups

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 ba...

On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.