Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular Cayley maps on dihedral groups with the smallest kernel   Let $\mathcal{M}=CM(D_n,X,p)$ be a regular Cayley map on the dihedral group
$D_n$ of order $2n, n \ge 2,$ and let $\pi$ be the power function associated
with $\mathcal{M}$. In this paper it is shown that the kernel Ker$(\pi)$ of the
power function $\pi$ is a dihedral subgroup of $D_n$ and if $n \ne 3,$ then the
kernel Ker$(\pi)$ is of order at least $4$. Moreover, all $\mathcal{M}$ are
classified for which Ker$(\pi)$ is of order $4$. In particular, besides $4$
sporadic maps on $4,4,8$ and $12$ vertices respectively, two infinite families
of non-$t$-balanced Cayley maps on $D_n$ are obtained.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex