On the $(S_2)$-condition of edge rings for cactus graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912246059237376 |
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| author | Dinu, Rodica Deepthi, Nayana Shibu |
| author_facet | Dinu, Rodica Deepthi, Nayana Shibu |
| contents | A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we will examine cactus graphs where all the blocks are $3$-cycles, i.e., triangular cactus graphs, of diameter $4$. Our main focus is to prove that the corresponding edge ring of this family of graphs is not normal and satisfies Serre's condition $(S_2)$. We use a criterion due to Katthän for non-normal affine semigroup rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $(S_2)$-condition of edge rings for cactus graphs Dinu, Rodica Deepthi, Nayana Shibu Commutative Algebra Combinatorics Primary : 13H10, Secondary: 52B20, 14M25 A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we will examine cactus graphs where all the blocks are $3$-cycles, i.e., triangular cactus graphs, of diameter $4$. Our main focus is to prove that the corresponding edge ring of this family of graphs is not normal and satisfies Serre's condition $(S_2)$. We use a criterion due to Katthän for non-normal affine semigroup rings. |
| title | On the $(S_2)$-condition of edge rings for cactus graphs |
| topic | Commutative Algebra Combinatorics Primary : 13H10, Secondary: 52B20, 14M25 |
| url | https://arxiv.org/abs/2402.17413 |