Perfect codes in 2-valent Cayley digraphs on abelian groups
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866929387629182976 |
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| author | Yu, Shilong Yang, Yuefeng Fan, Yushuang Ma, Xuanlong |
| author_facet | Yu, Shilong Yang, Yuefeng Fan, Yushuang Ma, Xuanlong |
| contents | For a digraph $Γ$, a subset $C$ of $V(Γ)$ is a perfect code if $C$ is a dominating set such that every vertex of $Γ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19017 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Perfect codes in 2-valent Cayley digraphs on abelian groups Yu, Shilong Yang, Yuefeng Fan, Yushuang Ma, Xuanlong Combinatorics For a digraph $Γ$, a subset $C$ of $V(Γ)$ is a perfect code if $C$ is a dominating set such that every vertex of $Γ$ 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. |
| title | Perfect codes in 2-valent Cayley digraphs on abelian groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2310.19017 |