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arXiv · 2505.19677

Perfect codes in quartic Cayley graphs of generalized dihedral groups

Chengcheng Dong·Yuefeng Yang·Changchang Dong
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Abstract

For a graph $Γ=(VΓ,EΓ)$, a subset $D$ of $VΓ$ is a perfect code in $Γ$ if every vertex of $Γ$ is dominated by exactly one vertex in $D$. In this paper, we classify all connected quartic Cayley graphs on generalized dihedral groups admitting a perfect code, and determine all perfect codes in such graphs.

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Chengcheng Dong, Yuefeng Yang, Changchang Dong. 2025-05-29. Perfect codes in quartic Cayley graphs of generalized dihedral groups. https://arxiv.org/abs/2505.19677

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