Cochordal zero divisor graphs and Betti numbers of their edge ideals
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908131158654976 |
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| author | Dung, Le Xuan Vu, Thanh |
| author_facet | Dung, Le Xuan Vu, Thanh |
| contents | We associate a sequence of positive integers, termed the type sequence, with a cochordal graph. Using this type sequence, we compute all graded Betti numbers of its edge ideal. We then classify all positive integer $n$ such that the zero divisor graph of $\mathbb{Z}/n \mathbb{Z}$ is cochordal and determine all the graded Betti numbers of its edge ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05251 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cochordal zero divisor graphs and Betti numbers of their edge ideals Dung, Le Xuan Vu, Thanh Commutative Algebra Combinatorics 13A70, 13D02, 05E40 We associate a sequence of positive integers, termed the type sequence, with a cochordal graph. Using this type sequence, we compute all graded Betti numbers of its edge ideal. We then classify all positive integer $n$ such that the zero divisor graph of $\mathbb{Z}/n \mathbb{Z}$ is cochordal and determine all the graded Betti numbers of its edge ideal. |
| title | Cochordal zero divisor graphs and Betti numbers of their edge ideals |
| topic | Commutative Algebra Combinatorics 13A70, 13D02, 05E40 |
| url | https://arxiv.org/abs/2411.05251 |