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arXiv · 2207.06743

Perfect codes in quintic Cayley graphs on abelian groups

Yuefeng Yang·Xuanlong Ma·Qing Zeng
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Abstract

A subset $C$ of the vertex set of a graph $Γ$ is called a perfect code of $Γ$ if every vertex of $Γ$ is at distance no more than one to exactly one vertex in $C$. In this paper, we classify all connected quintic Cayley graphs on abelian groups that admit a perfect code, and determine completely all perfect codes of such graphs.

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Yuefeng Yang, Xuanlong Ma, Qing Zeng. 2024-06-02. Perfect codes in quintic Cayley graphs on abelian groups. https://arxiv.org/abs/2207.06743

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