The existence of a $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$-factor based on the size or the $A_α$-spectral radius of graphs
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| Format: | Preprint |
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2024
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| _version_ | 1866915072452853760 |
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| author | Zhang, Xianglong You, Lihua |
| author_facet | Zhang, Xianglong You, Lihua |
| contents | Let $G$ be a connected graph of order $n$. A $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$-factor of $G$ is a spanning subgraph of $G$ such that each component is isomorphic to a member in $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$, where $\mathcal{T}(3)$ is a $\{1,2,3\}$-tree. The $A_α$-spectral radius of $G$ is denoted by $ρ_α(G)$. In this paper, we obtain a lower bound on the size or the $A_α$-spectral radius for $α\in[0,1)$ of $G$ to guarantee that $G$ has a $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$-factor, and construct an extremal graph to show that the bound on $A_α$-spectral radius is optimal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_11580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The existence of a $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$-factor based on the size or the $A_α$-spectral radius of graphs Zhang, Xianglong You, Lihua Combinatorics 05C50, 05C35 Let $G$ be a connected graph of order $n$. A $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$-factor of $G$ is a spanning subgraph of $G$ such that each component is isomorphic to a member in $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$, where $\mathcal{T}(3)$ is a $\{1,2,3\}$-tree. The $A_α$-spectral radius of $G$ is denoted by $ρ_α(G)$. In this paper, we obtain a lower bound on the size or the $A_α$-spectral radius for $α\in[0,1)$ of $G$ to guarantee that $G$ has a $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$-factor, and construct an extremal graph to show that the bound on $A_α$-spectral radius is optimal. |
| title | The existence of a $\{P_{2},C_{3},P_{5},\mathcal{T}(3)\}$-factor based on the size or the $A_α$-spectral radius of graphs |
| topic | Combinatorics 05C50, 05C35 |
| url | https://arxiv.org/abs/2412.11580 |