Regular t-balanced Cayley maps

Authors:
Marston Conder;Robert Jajcay;Tom Tucker
Affiliations:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand;Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN 47809, USA;Mathematics Department, Colgate University, Hamilton, NY 13346, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2007

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Abstract

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. Siran, M. Skoviera, Groups with sign structure and their antiautomorphisms, Discrete Math. 108 (1992) 189-202. [12]]). We develop a general theory of t-balanced Cayley maps based on the use of skew-morphisms of groups [R. Jajcay, J. Siran, Skew-morphisms of regular Cayley maps, Discrete Math. 244 (1-3) (2002) 167-179], and apply our results to the specific case of regular Cayley maps of abelian groups.