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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2502.00405 |
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| _version_ | 1866916593563336704 |
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| author | Ren, Fengyun Zhang, Shumin Wang, Ke |
| author_facet | Ren, Fengyun Zhang, Shumin Wang, Ke |
| contents | The $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor of a graph is a spanning subgraph whose each component is an element of $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a $\{K_2\}$-factor. We get a lower bound on the size (resp. the spectral radius) of $G$ to guarantee that $G$ contains a $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor. Then we determine an upper bound on the distance spectral radius of $G$ to ensure that $G$ has a $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Sufficient Conditions for Graph Factors Ren, Fengyun Zhang, Shumin Wang, Ke Combinatorics Discrete Mathematics The $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor of a graph is a spanning subgraph whose each component is an element of $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a $\{K_2\}$-factor. We get a lower bound on the size (resp. the spectral radius) of $G$ to guarantee that $G$ contains a $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor. Then we determine an upper bound on the distance spectral radius of $G$ to ensure that $G$ has a $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible. |
| title | Spectral Sufficient Conditions for Graph Factors |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2502.00405 |