We present a theory of Cayley maps, ie, embeddings of Cayley graphs into oriented
surfaces having the same cyclic rotation of generators around each vertex. These maps …

A Cayley map M is a 2-cell embedding of a Cayley graph in an orientable surface with the
same orientation (the induced permutation of generators) at each vertex. The concept of a …

Recently, regular Cayley maps of cyclic groups and dihedral groups have been classified in
[7] and [20], respectively. A nature question is to classify regular Cayley maps of elementary …

This paper aims to develop a theory for studying Cayley graphs, especially for those with a
high degree of symmetry. The theory consists of analysing several types of basic Cayley …

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 …

The concept of a t-balanced Cayley map is a natural generalization of the previously studied
notions of balanced and anti-balanced Cayley maps (the terms coined by [J. Širáň, M …

An orientably-regular map M is a 2-cell embedding of a finite connected graph in a closed
orientable surface such that the group Aut∘ M of orientation-preserving automorphisms of M …

In their study of regular t-balanced Cayley maps on a group, Conder et al.[M. Conder, R.
Jajcay, T. Tucker, Regular t-balanced Cayley maps, J. Combin. Theory Ser. B (in press)] …

The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-
balanced skew-morphisms of regular Cayley maps which are in turn generalizations of …

A Cayley map M= CM (G, X, p) is t-balanced if p (x)− 1= pt (x− 1) for all x∈ X. Recently,
Conder et al. classified the regular anti-balanced Cayley maps for abelian groups and Kwak …