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Let $R$ be the Ehrhart ring of the stable set polytope of a cycle graph whichis not Gorenstein. We describe the non-Gorenstein locus of $\mathrm{Spec} R$.Further, we show that $R$ is almost Gorenstein. Moreover, we show that theconjecture of Hibi and Tsuchiya is true.

Non-Gorenstein locus and almost Gorenstein property of the Ehrhart ring of the stable set polytope of a cycle graph