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arXiv · 2503.10994

Normal and non-normal Cayley digraphs on cyclic and dihedral groups

Jun-Feng Yang·Yan-Quan Feng·Fu-Gang Yin·Jin-Xin Zhou
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Abstract

A Cayley digraph on a group $G$ is called NNN if the Cayley digraph is normal and its automorphism group contains a non-normal regular subgroup isomorphic to $G$. A group is called NNND-group or NNN-group if there is an NNN Cayley digraph or graph on the group, respectively. In this paper, it is shown that there is no cyclic NNND-group, and hence no cyclic NNN-group. Furthermore, a dihedral group of order $2n$ is an NNND-group or an NNN-group if and only if $n\ge 6$ is even and $n\not=8$.

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Jun-Feng Yang, Yan-Quan Feng, Fu-Gang Yin, Jin-Xin Zhou. 2025-03-14. Normal and non-normal Cayley digraphs on cyclic and dihedral groups. https://arxiv.org/abs/2503.10994

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