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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2512.19233 |
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| _version_ | 1866917163432935424 |
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| author | Luo, Yi-Lu Deng, Yun-Ping Sun, Yuan |
| author_facet | Luo, Yi-Lu Deng, Yun-Ping Sun, Yuan |
| contents | Let $G = (V(G), E(G))$ be a simple connected graph and $Ω$ a subset of $ V(G)$ with $|Ω|\geq2$. An $Ω$-path in $G$ is a path that connects all vertices of $Ω$. Two $Ω$-paths $P_i$ and $P_j$ are said to be internally disjoint if $V(P_i)\cap V(P_j)=Ω$ and $E(P_i)\cap E(P_j)=\emptyset$. Denote $π_G(Ω)$ by the maximum number of internally disjoint $Ω$-paths in $G$. For an integer $k\geq2$, the $k$-path-connectivity $π_k(G)$ of $G$ is defined as $\min\{π_G(Ω)\midΩ\subseteq V(G)$ and $|Ω|=k\}$. Let $CW_n$ denote the Cayley graph generated by the $n$-vertex wheel graph. In this paper, we investigate the $3$-path-connectivity of $CW_n$ and prove that $π_3(CW_n)=\lfloor\frac{6n-9}4\rfloor$ for all $n\geq4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 3-path-connectivity of Cayley graphs generated by wheel graphs Luo, Yi-Lu Deng, Yun-Ping Sun, Yuan Combinatorics Let $G = (V(G), E(G))$ be a simple connected graph and $Ω$ a subset of $ V(G)$ with $|Ω|\geq2$. An $Ω$-path in $G$ is a path that connects all vertices of $Ω$. Two $Ω$-paths $P_i$ and $P_j$ are said to be internally disjoint if $V(P_i)\cap V(P_j)=Ω$ and $E(P_i)\cap E(P_j)=\emptyset$. Denote $π_G(Ω)$ by the maximum number of internally disjoint $Ω$-paths in $G$. For an integer $k\geq2$, the $k$-path-connectivity $π_k(G)$ of $G$ is defined as $\min\{π_G(Ω)\midΩ\subseteq V(G)$ and $|Ω|=k\}$. Let $CW_n$ denote the Cayley graph generated by the $n$-vertex wheel graph. In this paper, we investigate the $3$-path-connectivity of $CW_n$ and prove that $π_3(CW_n)=\lfloor\frac{6n-9}4\rfloor$ for all $n\geq4$. |
| title | 3-path-connectivity of Cayley graphs generated by wheel graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.19233 |