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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.15141 |
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| _version_ | 1866909302027976704 |
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| author | Hibi, Takayuki Madani, Sara Saeedi |
| author_facet | Hibi, Takayuki Madani, Sara Saeedi |
| contents | Let $G$ be a finite simple non-complete connected graph on $[n] = \{1, \ldots, n\}$ and $κ(G) \geq 1$ its vertex connectivity. Let $f(G)$ denote the number of free vertices of $G$ and $\mathrm{diam}(G)$ the diameter of $G$. The final goal of this paper is to determine all sequences of integers $(n,f,d,k)$ with $n\geq 8$, $f\geq 0$, $d\geq 2$ and $k\geq 1$ for which there exists a finite simple non-complete connected graph on $[n]$ with $f=f(G)$, $d=\mathrm{diam}(G)$ and $k=κ(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15141 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diameter and connectivity of finite simple graphs II Hibi, Takayuki Madani, Sara Saeedi Combinatorics 05C12, 05C40 Let $G$ be a finite simple non-complete connected graph on $[n] = \{1, \ldots, n\}$ and $κ(G) \geq 1$ its vertex connectivity. Let $f(G)$ denote the number of free vertices of $G$ and $\mathrm{diam}(G)$ the diameter of $G$. The final goal of this paper is to determine all sequences of integers $(n,f,d,k)$ with $n\geq 8$, $f\geq 0$, $d\geq 2$ and $k\geq 1$ for which there exists a finite simple non-complete connected graph on $[n]$ with $f=f(G)$, $d=\mathrm{diam}(G)$ and $k=κ(G)$. |
| title | Diameter and connectivity of finite simple graphs II |
| topic | Combinatorics 05C12, 05C40 |
| url | https://arxiv.org/abs/2408.15141 |