Extremal distance spectral radius of graphs with $h$-extra $r$-component connectivity
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908561607491584 |
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| author | Zhang, Daoxia Li, Dan Ding, Wenxiu |
| author_facet | Zhang, Daoxia Li, Dan Ding, Wenxiu |
| contents | For two integers $r\geq 2$ and $h\geq 0$, the $h$-extra $r$-component connectivity of a graph $G$, denoted by $cκ_{r}^{h}$, is defined as the minimum number of vertices whose removal produces a disconnected graph with at least $r$ components, where each component contains at least $h+1$ vertices. Let $\mathcal{G}_{n,δ}^{cκ_{r}^{h}}$ represent the set of graphs of order $n$ with minimum degree $δ$ and $h$-extra $r$-component connectivity $cκ_{r}^{h}$. Hu, Lin, and Zhang [\textit{Discrete Math.} \textbf{345} (2025) 114621] investigated the case when $h=0$ within $\mathcal{G}_{n,δ}^{cκ_{r}^{h}}$, and characterized the corresponding extremal graphs that minimize the distance spectral radius. In this paper, we further explore the relevant extremal graphs in $\mathcal{G}_{n,δ}^{cκ_{r}^{h}}$ for $h\geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremal distance spectral radius of graphs with $h$-extra $r$-component connectivity Zhang, Daoxia Li, Dan Ding, Wenxiu Combinatorics For two integers $r\geq 2$ and $h\geq 0$, the $h$-extra $r$-component connectivity of a graph $G$, denoted by $cκ_{r}^{h}$, is defined as the minimum number of vertices whose removal produces a disconnected graph with at least $r$ components, where each component contains at least $h+1$ vertices. Let $\mathcal{G}_{n,δ}^{cκ_{r}^{h}}$ represent the set of graphs of order $n$ with minimum degree $δ$ and $h$-extra $r$-component connectivity $cκ_{r}^{h}$. Hu, Lin, and Zhang [\textit{Discrete Math.} \textbf{345} (2025) 114621] investigated the case when $h=0$ within $\mathcal{G}_{n,δ}^{cκ_{r}^{h}}$, and characterized the corresponding extremal graphs that minimize the distance spectral radius. In this paper, we further explore the relevant extremal graphs in $\mathcal{G}_{n,δ}^{cκ_{r}^{h}}$ for $h\geq 1$. |
| title | Extremal distance spectral radius of graphs with $h$-extra $r$-component connectivity |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.22538 |