Open Neighborhood Ideals of Well-Totally Dominated Trees are Cohen-Macaulay
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915797608169472 |
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| author | Lim, Jounglag Gossell, James Sather-Wagstaff, Keri Ann |
| author_facet | Lim, Jounglag Gossell, James Sather-Wagstaff, Keri Ann |
| contents | We introduce and investigate the open neighborhood ideal $\mathcal{N}(G)$ of a finite simple graph $G$. We describe the minimal primary decomposition of $\mathcal{N}(G)$ in terms of the minimal total dominating sets (TDSs) of $G$. Then we prove that the open neighborhood ideal of a tree is Cohen-Macaulay if and only if the tree is well-totally dominated (WTD) and calculate the Cohen-Macaulay type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Open Neighborhood Ideals of Well-Totally Dominated Trees are Cohen-Macaulay Lim, Jounglag Gossell, James Sather-Wagstaff, Keri Ann Commutative Algebra Primary: 13F55, 13H10, Secondary: 05C05, 05C69, 05E40 We introduce and investigate the open neighborhood ideal $\mathcal{N}(G)$ of a finite simple graph $G$. We describe the minimal primary decomposition of $\mathcal{N}(G)$ in terms of the minimal total dominating sets (TDSs) of $G$. Then we prove that the open neighborhood ideal of a tree is Cohen-Macaulay if and only if the tree is well-totally dominated (WTD) and calculate the Cohen-Macaulay type. |
| title | Open Neighborhood Ideals of Well-Totally Dominated Trees are Cohen-Macaulay |
| topic | Commutative Algebra Primary: 13F55, 13H10, Secondary: 05C05, 05C69, 05E40 |
| url | https://arxiv.org/abs/2510.19707 |