A CLASSIFICATION OF REGULAR T-BALANCED CAYLEY MAPS ON DICYCLIC GROUPS

Abstract

A Cayley map CM(G, S, p) is a 2-cell embedding of a Cayley graph Cay(G, S) into an orientable surface such that all vertex-rotations correspond to the cyclic permutation p of the generating set S. It is called regular if its automorphism group acts regularly on the dart set. A regular Cayley map M = CM(G, S, p) is called t-balanced if p(x)(-1) = p(t) (x(-1)) for every x is an element of S. In this paper, we classify the regular t-balanced Cayley maps on dicyclic groups for all t. As a result, all such maps are 1-balanced. (c) 2007 Elsevier Ltd. All rights reserved.