The maximum number of maximum dissociation sets in potted graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916114849595392 |
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| author | Huang, Zejun Zhang, Xinwei |
| author_facet | Huang, Zejun Zhang, Xinwei |
| contents | A potted graph is a unicyclic graph such that its cycle contains a unique vertex with degree larger than 2. Given a graph $G$, a subset of $V(G)$ is a dissociation set of $G$ if it induces a subgraph with maximum degree at most one. A maximum dissociation set is a dissociation set with maximum cardinality. In this paper, we determine the maximum number of maximum dissociation sets in a potted graph of order $n$ which contains a fixed cycle. Extremal potted graphs attaining this maximum number are also characterized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The maximum number of maximum dissociation sets in potted graphs Huang, Zejun Zhang, Xinwei Combinatorics A potted graph is a unicyclic graph such that its cycle contains a unique vertex with degree larger than 2. Given a graph $G$, a subset of $V(G)$ is a dissociation set of $G$ if it induces a subgraph with maximum degree at most one. A maximum dissociation set is a dissociation set with maximum cardinality. In this paper, we determine the maximum number of maximum dissociation sets in a potted graph of order $n$ which contains a fixed cycle. Extremal potted graphs attaining this maximum number are also characterized. |
| title | The maximum number of maximum dissociation sets in potted graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.02458 |