A note on the second-largest number of dissociation sets in connected graphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915559065518080 |
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| author | Li, Pingshan Yang, Ke Jin, Wei |
| author_facet | Li, Pingshan Yang, Ke Jin, Wei |
| contents | A subset of vertices is called a dissociation set if it induces a subgraph with vertex degree at most one. Recently, Yuan et al. established the upper bound of the maximum number of dissociation sets among all connected graphs of order n and characterized the corresponding extremal graphs.They also proposed a question regarding the second-largest number of dissociation sets among all connected graphs of order n and the corresponding extremal graphs. In this paper, we give a positive answer to this question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12740 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the second-largest number of dissociation sets in connected graphs Li, Pingshan Yang, Ke Jin, Wei Combinatorics A subset of vertices is called a dissociation set if it induces a subgraph with vertex degree at most one. Recently, Yuan et al. established the upper bound of the maximum number of dissociation sets among all connected graphs of order n and characterized the corresponding extremal graphs.They also proposed a question regarding the second-largest number of dissociation sets among all connected graphs of order n and the corresponding extremal graphs. In this paper, we give a positive answer to this question. |
| title | A note on the second-largest number of dissociation sets in connected graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.12740 |