Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A classification of prime-valent regular Cayley maps on some groups   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.

23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin