Perfect codes in quintic Cayley graphs on abelian groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917680949231616 |
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| author | Yang, Yuefeng Ma, Xuanlong Zeng, Qing |
| author_facet | Yang, Yuefeng Ma, Xuanlong Zeng, Qing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06743 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Perfect codes in quintic Cayley graphs on abelian groups Yang, Yuefeng Ma, Xuanlong Zeng, Qing Combinatorics 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. |
| title | Perfect codes in quintic Cayley graphs on abelian groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2207.06743 |