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

Title
A CLASSIFICATION OF PRIME-VALENT REGULAR CAYLEY MAPS ON ABELIAN, DIHEDRAL AND DICYCLIC GROUPS
Author(s)
권영수이재운김동석[김동석]
Keywords
GRAPHS
Issue Date
201001
Publisher
KOREAN MATHEMATICAL SOC
Citation
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.47, no.1, pp.17 - 27
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.
URI
http://hdl.handle.net/YU.REPOSITORY/23004http://dx.doi.org/10.4134/BKMS.2010.47.1.017
ISSN
1015-8634
Appears in Collections:
이과대학 > 수학과 > Articles
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