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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.03746 |
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| _version_ | 1866915429742542848 |
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| author | Duan, Xinhui Lu, Lu |
| author_facet | Duan, Xinhui Lu, Lu |
| contents | For a cycle $C_k$ on $k$ vertices, its $p$-th power, denoted $C_k^p$, is the graph obtained by adding edges between all pairs of vertices at distance at most $p$ in $C_k$. Let $\ex(n, F)$ and $\spex(n, F)$ denote the maximum possible number of edges and the maximum possible spectral radius, respectively, among all $n$-vertex $F$-free graphs. In this paper, we determine precisely the unique extremal graph achieving $\ex(n, C_k^p)$ and $\spex(n, C_k^p)$ for sufficiently large $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral extremal problem of the $p$th power of cycles Duan, Xinhui Lu, Lu Combinatorics 05C50 For a cycle $C_k$ on $k$ vertices, its $p$-th power, denoted $C_k^p$, is the graph obtained by adding edges between all pairs of vertices at distance at most $p$ in $C_k$. Let $\ex(n, F)$ and $\spex(n, F)$ denote the maximum possible number of edges and the maximum possible spectral radius, respectively, among all $n$-vertex $F$-free graphs. In this paper, we determine precisely the unique extremal graph achieving $\ex(n, C_k^p)$ and $\spex(n, C_k^p)$ for sufficiently large $n$. |
| title | Spectral extremal problem of the $p$th power of cycles |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2508.03746 |