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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2511.22089 |
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| _version_ | 1866918451228966912 |
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| author | Waghmare, P. Joshi, V. |
| author_facet | Waghmare, P. Joshi, V. |
| contents | In this paper, we prove that the zero-divisor graph $Γ(P)$ of a Boolean poset $P$ is both well-covered and Cohen--Macaulay. Furthermore, for a poset $\mathbf{P} = \prod_{i=1}^{n} P_i$ $(n \ge 3)$, where each $P_i$ is a finite bounded poset satisfying $Z(P_i) = \{0\}$ for all $i$, and $\le |P_1| \le |P_2| \le \cdots \le |P_n|, $ we show that the zero-divisor graph $Γ(\mathbf{P})$ is Cohen--Macaulay if and only if $\mathbf{P}$ is a Boolean lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22089 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohen-Macauleyness of the Zero-Divisor Graph of a Boolean Poset Waghmare, P. Joshi, V. Combinatorics 06E20, 13A70, 13C14 In this paper, we prove that the zero-divisor graph $Γ(P)$ of a Boolean poset $P$ is both well-covered and Cohen--Macaulay. Furthermore, for a poset $\mathbf{P} = \prod_{i=1}^{n} P_i$ $(n \ge 3)$, where each $P_i$ is a finite bounded poset satisfying $Z(P_i) = \{0\}$ for all $i$, and $\le |P_1| \le |P_2| \le \cdots \le |P_n|, $ we show that the zero-divisor graph $Γ(\mathbf{P})$ is Cohen--Macaulay if and only if $\mathbf{P}$ is a Boolean lattice. |
| title | Cohen-Macauleyness of the Zero-Divisor Graph of a Boolean Poset |
| topic | Combinatorics 06E20, 13A70, 13C14 |
| url | https://arxiv.org/abs/2511.22089 |