Spectral radius of $2$-dimensional simplicial complexes with given Betti number
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915725825802240 |
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| author | She, Chuan-Ming Fan, Yi-Zheng Song, Yi-Min |
| author_facet | She, Chuan-Ming Fan, Yi-Zheng Song, Yi-Min |
| contents | In this paper we establish an asymptotic formula for the signless Laplacian spectral radius of a $2$-dimensional simplicial complex with given $2$-th Betti number. Furthermore, we characterize the $2$-dimensional simplicial complex that achieves the maximum signless Laplacian spectral radius among all-dimensional simplicial complex with the $2$-th Betti number equal to $1$ or $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08171 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral radius of $2$-dimensional simplicial complexes with given Betti number She, Chuan-Ming Fan, Yi-Zheng Song, Yi-Min Combinatorics Primary 05C35, 05E45, Secondary 05C65, 55U05 In this paper we establish an asymptotic formula for the signless Laplacian spectral radius of a $2$-dimensional simplicial complex with given $2$-th Betti number. Furthermore, we characterize the $2$-dimensional simplicial complex that achieves the maximum signless Laplacian spectral radius among all-dimensional simplicial complex with the $2$-th Betti number equal to $1$ or $2$. |
| title | Spectral radius of $2$-dimensional simplicial complexes with given Betti number |
| topic | Combinatorics Primary 05C35, 05E45, Secondary 05C65, 55U05 |
| url | https://arxiv.org/abs/2601.08171 |