Classification of perfect and total perfect codes in generalized Petersen graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908905140912128 |
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| author | Wang, Xiaomeng Zhang, Junyang |
| author_facet | Wang, Xiaomeng Zhang, Junyang |
| contents | In a graph $Γ$, a perfect code is an independent set $C$ with the property that every vertex not in $C$ is adjacent to a unique vertex in $C$, and a total perfect code is a set $C$ of vertices of $Γ$ such that every vertex of $Γ$ is adjacent to a unique vertex in $C$. We classify these codes for generalized Petersen graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20722 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of perfect and total perfect codes in generalized Petersen graphs Wang, Xiaomeng Zhang, Junyang Combinatorics In a graph $Γ$, a perfect code is an independent set $C$ with the property that every vertex not in $C$ is adjacent to a unique vertex in $C$, and a total perfect code is a set $C$ of vertices of $Γ$ such that every vertex of $Γ$ is adjacent to a unique vertex in $C$. We classify these codes for generalized Petersen graphs. |
| title | Classification of perfect and total perfect codes in generalized Petersen graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.20722 |