On Gorenstein Circulant Graphs and Gorenstein SQC Graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866910405321818112 |
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| author | Nikseresht, Ashkan Oboudi, Mohammad Reza |
| author_facet | Nikseresht, Ashkan Oboudi, Mohammad Reza |
| contents | We characterize some graphs with a Gorenstein edge ideal. In particular, we show that if $G$ is a circulant graph with vertex degree at most four or a circulant graph of the form $C_n(1,\ldots, d)$ for some $d\leq n/2$, then $G$ is Gorenstein if and only if $G\cong tK_2$, $G\cong t\overline{C_n}$ or $G\cong tC_{13}(1,5)$ for some integers $t$ and $n\geq 4$. Also we prove that if $G$ is a \mathcal{SQC}\ graph, then $G$ is Gorenstein if and only if each component of $G$ is either an edge or a 5-cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_11497 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On Gorenstein Circulant Graphs and Gorenstein SQC Graphs Nikseresht, Ashkan Oboudi, Mohammad Reza Commutative Algebra Combinatorics 13F55, 13H10, 05E40, 05C25 We characterize some graphs with a Gorenstein edge ideal. In particular, we show that if $G$ is a circulant graph with vertex degree at most four or a circulant graph of the form $C_n(1,\ldots, d)$ for some $d\leq n/2$, then $G$ is Gorenstein if and only if $G\cong tK_2$, $G\cong t\overline{C_n}$ or $G\cong tC_{13}(1,5)$ for some integers $t$ and $n\geq 4$. Also we prove that if $G$ is a \mathcal{SQC}\ graph, then $G$ is Gorenstein if and only if each component of $G$ is either an edge or a 5-cycle. |
| title | On Gorenstein Circulant Graphs and Gorenstein SQC Graphs |
| topic | Commutative Algebra Combinatorics 13F55, 13H10, 05E40, 05C25 |
| url | https://arxiv.org/abs/1906.11497 |