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arXiv · 1906.11497

On Gorenstein Circulant Graphs and Gorenstein SQC Graphs

Ashkan Nikseresht·Mohammad Reza Oboudi
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Abstract

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.

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Ashkan Nikseresht, Mohammad Reza Oboudi. 2019-06-27. On Gorenstein Circulant Graphs and Gorenstein SQC Graphs. https://doi.org/10.1016/j.disc.2023.113472

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