The $K_{1,2}$-structure-connectivity of graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910365536747520 |
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| author | Zhao, Xiao Zheng, Haojie Li, Hengzhe |
| author_facet | Zhao, Xiao Zheng, Haojie Li, Hengzhe |
| contents | In this paper, we mainly investigate $K_{1,2}$-structure-connectivity for any connected graph. Let $G$ be a connected graph with $n$ vertices, we show that $κ(G; K_{1,2})$ is well-defined if $diam(G)\geq 4$, or $n\equiv 1\pmod 3$, or $G\notin \{C_{5},K_{n}\}$ when $n\equiv 2\pmod 3$, or there exist three vertices $u,v,w$ such that $N_{G}(u)\cap (N_{G}(v,w)\cup\{v,w\})=\emptyset$ when $n\equiv 0\pmod 3$. Furthermore, if $G$ has $K_{1,2}$-structure-cut, we prove $κ(G)/3\leqκ(G; K_{1,2})\leqκ(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $K_{1,2}$-structure-connectivity of graphs Zhao, Xiao Zheng, Haojie Li, Hengzhe Combinatorics In this paper, we mainly investigate $K_{1,2}$-structure-connectivity for any connected graph. Let $G$ be a connected graph with $n$ vertices, we show that $κ(G; K_{1,2})$ is well-defined if $diam(G)\geq 4$, or $n\equiv 1\pmod 3$, or $G\notin \{C_{5},K_{n}\}$ when $n\equiv 2\pmod 3$, or there exist three vertices $u,v,w$ such that $N_{G}(u)\cap (N_{G}(v,w)\cup\{v,w\})=\emptyset$ when $n\equiv 0\pmod 3$. Furthermore, if $G$ has $K_{1,2}$-structure-cut, we prove $κ(G)/3\leqκ(G; K_{1,2})\leqκ(G)$. |
| title | The $K_{1,2}$-structure-connectivity of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2403.06752 |