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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| creator | Yu, Shilong Yang, Yuefeng Fan, Yushuang Ma, Xuanlong |
| description | 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_str_mv | 10.48550/arxiv.2310.19017 |
| format | Article |
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is a dominating set such that every vertex of $\Gamma$ is dominated by exactly
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| subjects | Mathematics - Combinatorics |
| title | Perfect codes in 2-valent Cayley digraphs on abelian groups |
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