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http://dx.doi.org/10.4134/BKMS.2010.47.1.017

A CLASSIFICATION OF PRIME-VALENT REGULAR CAYLEY MAPS ON ABELIAN, DIHEDRAL AND DICYCLIC GROUPS  

Kim, Dong-Seok (Department of Mathematics, Kyunggi University)
Kwon, Young-Soo (Department of Mathematics, Yeungnam University)
Lee, Jae-Un (Department of Mathematics, Yeungnam University)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.1, 2010 , pp. 17-27 More about this Journal
Abstract
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 balanced and all prime-valent regular Cayley maps on abelian groups are either balanced or anti-balanced. Furthermore, we prove that there is no prime-valent regular Cayley map on any dicyclic group.
Keywords
Cayley map; regular embedding;
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