Associated primes of the second power of closed neighborhood ideals of graphs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913938431541248 |
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| author | Hien, Ha Thi Thu Vu, Thanh |
| author_facet | Hien, Ha Thi Thu Vu, Thanh |
| contents | We study simple graphs for which the maximal homogeneous ideal is an associated prime of the second power of their closed neighborhood ideals. In particular, we show that such graphs must have diameter at most $6$, and that those with diameter $2$ must be vertex diameter-$2$-critical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Associated primes of the second power of closed neighborhood ideals of graphs Hien, Ha Thi Thu Vu, Thanh Commutative Algebra Combinatorics 13C15, 13F55 We study simple graphs for which the maximal homogeneous ideal is an associated prime of the second power of their closed neighborhood ideals. In particular, we show that such graphs must have diameter at most $6$, and that those with diameter $2$ must be vertex diameter-$2$-critical. |
| title | Associated primes of the second power of closed neighborhood ideals of graphs |
| topic | Commutative Algebra Combinatorics 13C15, 13F55 |
| url | https://arxiv.org/abs/2507.08777 |