Let G be the circulant graph CnS with S ? {1, 2},...,[n/2]}, and let I(G) denote the edge ideal in the ring R = k[x_1,..., x_n]. We consider the problem of determining when G is Cohen-Macaulay, i.e, R/I(G) is a Cohen-Macaulay ring. Because a Cohen-Macaulay graph G must be well-covered, we focus on known families of wellcovered circulant graphs of the form C_n(1, 2,...,d). We also characterize which cubic circulant graphs are Cohen-Macaulay. We end with the observation that even though the well-covered property is preserved under lexicographical products of graphs, this is not true of the Cohen-Macaulay property.
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机译：设G为S的循环图CnS。 {1，2}，...，[n / 2]}，令I（G）表示环R = k [x_1，...，x_n]中的边缘理想。我们考虑确定G何时为Cohen-Macaulay环，即R / I（G）为Cohen-Macaulay环的问题。由于必须很好地覆盖Cohen-Macaulay图G，因此我们将重点放在形式为C_n（1,2，...，d）的已知的覆盖良好的循环图族上。我们还表征了哪些三次循环图是科恩-马考莱。我们以观察得出结论，即使将充分覆盖的属性保留在图的词典产品之下，但对于Cohen-Macaulay属性却并非如此。
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