Perfect codes in Cayley graphs of abelian groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910227084869632 |
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| author | Cameron, Peter J. Yap, Roro Sihui Zhou, Sanming |
| author_facet | Cameron, Peter J. Yap, Roro Sihui Zhou, Sanming |
| contents | A perfect code in a graph $Γ= (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A total perfect code in $Γ$ is a subset $C$ of $V$ such that every vertex of $Γ$ is adjacent to exactly one vertex in $C$. In this paper we prove several results on perfect codes and total perfect codes in Cayley graphs of finite abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perfect codes in Cayley graphs of abelian groups Cameron, Peter J. Yap, Roro Sihui Zhou, Sanming Combinatorics 05C25, 05C69, 94B25 A perfect code in a graph $Γ= (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A total perfect code in $Γ$ is a subset $C$ of $V$ such that every vertex of $Γ$ is adjacent to exactly one vertex in $C$. In this paper we prove several results on perfect codes and total perfect codes in Cayley graphs of finite abelian groups. |
| title | Perfect codes in Cayley graphs of abelian groups |
| topic | Combinatorics 05C25, 05C69, 94B25 |
| url | https://arxiv.org/abs/2507.11871 |