Skew-morphisms of regular Cayley maps

Jajcay, R. and Siran, J. (2002). Skew-morphisms of regular Cayley maps. Discrete Mathematics, 244(1-3) pp. 167–179.

DOI: https://doi.org/10.1016/S0012-365X(01)00081-4

Abstract

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 skew-morphism generalizes several concepts previously studied with respect to regular Cayley maps, and allows for a unified theory of regular Cayley maps and their automorphism groups. Using algebraic properties of skew-morphisms of groups we reprove or extend some previously known results and obtain several new ones.

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