The characteristic polynomials of $r$-uniform hypercycles with length $l$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915240347697152 |
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| author | Bo, Dong Cunxiang, Duan Ligong, Wang |
| author_facet | Bo, Dong Cunxiang, Duan Ligong, Wang |
| contents | Let $C_{l}$ be a cycle with length $l.$ The $r$-uniform hypercycle with length $l$ is obtained by adding $r-2$ new vertices in every edge of $C_{l},$ denoted by $C_l^{(r)}$. In this paper, we deduce some higher-order traces for the adjacent tensor of $C_l^{(r)}$ by BEST Theorem. Then we obtain higher-order spectral moments according to the relationship between eigenvalues of power hypergraphs and eigenvalues of signed graphs. Finally, the general expression of the characteristic polynomials of $C_l^{(r)}$ is given. Furthermore, by using this general expression, we present the characteristic polynomials of $C_5^{(r)}$ and $C_6^{(r)}$ as examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The characteristic polynomials of $r$-uniform hypercycles with length $l$ Bo, Dong Cunxiang, Duan Ligong, Wang Combinatorics G.2.2, F.2.2 G.2.2; F.2.2 Let $C_{l}$ be a cycle with length $l.$ The $r$-uniform hypercycle with length $l$ is obtained by adding $r-2$ new vertices in every edge of $C_{l},$ denoted by $C_l^{(r)}$. In this paper, we deduce some higher-order traces for the adjacent tensor of $C_l^{(r)}$ by BEST Theorem. Then we obtain higher-order spectral moments according to the relationship between eigenvalues of power hypergraphs and eigenvalues of signed graphs. Finally, the general expression of the characteristic polynomials of $C_l^{(r)}$ is given. Furthermore, by using this general expression, we present the characteristic polynomials of $C_5^{(r)}$ and $C_6^{(r)}$ as examples. |
| title | The characteristic polynomials of $r$-uniform hypercycles with length $l$ |
| topic | Combinatorics G.2.2, F.2.2 G.2.2; F.2.2 |
| url | https://arxiv.org/abs/2504.09487 |