Perfect codes in 2-valent Cayley digraphs on abelian groups

Perfect codes in 2-valent Cayley digraphs on abelian groups

For a digraph $\Gamma$, a subset $C$ of $V(\Gamma)$ is a perfect code if $C$ is a dominating set such that every vertex of $\Gamma$ is dominated by exactly one vertex in $C$. In this paper, we classify strongly connected 2-valent Cayley digraphs on abelian groups admitting a perfect code, and determ...

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Hauptverfasser: Yu, Shilong, Yang, Yuefeng, Fan, Yushuang, Ma, Xuanlong
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
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Zusammenfassung:For a digraph $\Gamma$, a subset $C$ of $V(\Gamma)$ is a perfect code if $C$ is a dominating set such that every vertex of $\Gamma$ is dominated by exactly one vertex in $C$. In this paper, we classify strongly connected 2-valent Cayley digraphs on abelian groups admitting a perfect code, and determine completely all perfect codes of such digraphs.
DOI:10.48550/arxiv.2310.19017