The minimum number of maximal dissociation sets in unicyclic graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917828997677056 |
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| author | Zhang, Junxia Ren, Xiangyu Wang, Maoqun |
| author_facet | Zhang, Junxia Ren, Xiangyu Wang, Maoqun |
| contents | A subset of vertices in a graph $G$ is considered a maximal dissociation set if it induces a subgraph with vertex degree at most 1 and it is not contained within any other dissociation sets. In this paper, it is shown that for $n\geq 3$, every unicyclic graph contains a minimum of $\lfloor n/2\rfloor+2$ maximal dissociation sets. We also show the graphs that attain this minimum bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The minimum number of maximal dissociation sets in unicyclic graphs Zhang, Junxia Ren, Xiangyu Wang, Maoqun Combinatorics A subset of vertices in a graph $G$ is considered a maximal dissociation set if it induces a subgraph with vertex degree at most 1 and it is not contained within any other dissociation sets. In this paper, it is shown that for $n\geq 3$, every unicyclic graph contains a minimum of $\lfloor n/2\rfloor+2$ maximal dissociation sets. We also show the graphs that attain this minimum bound. |
| title | The minimum number of maximal dissociation sets in unicyclic graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.02918 |