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Some Combinatorial Characterizations of Gorenstein Graphs with Independence Number Less Than Four
Iranian Journal of Science and Technology, Transactions A: Science ( IF 1.4 ) Pub Date : 2020-08-28 , DOI: 10.1007/s40995-020-00961-w
Mohammad Reza Oboudi , Ashkan Nikseresht

Let \(\alpha =\alpha (G)\) be the independence number of a simple graph G with n vertices and I(G) be its edge ideal in \(S=K[x_1,\ldots , x_n]\). If S/I(G) is Gorenstein, the graph G is called Gorenstein over K, and if G is Gorenstein over every field, then we simply say that G is Gorenstein. In this article, first we state a condition equivalent to G being Gorenstein, and using this, we give a characterization of Gorenstein graphs with \(\alpha =2\). Then, we present some properties of Gorenstein graphs with \(\alpha =3\), and as an application of these results, we characterize triangle-free Gorenstein graphs with \(\alpha =3\).



中文翻译:

具有小于4的独立数的Gorenstein图的一些组合刻画

\(\ alpha = \ alpha(G)\)是具有n个顶点的简单图G的独立性,而IG)是\(S = K [x_1,\ ldots,x_n] \)中的边缘理想。如果S / IG)是Gorenstein,则图GK上称为Gorenstein ,如果G在每个域上都是Gorenstein,则我们简单地说G是Gorenstein。在本文中,首先我们陈述一个等于G为Gorenstein的条件,并使用它给出\(\ alpha = 2 \)的Gorenstein图的特征。。然后,我们展示具有\(\ alpha = 3 \)的Gorenstein图的一些性质,并作为这些结果的应用,我们描述具有\(\ alpha = 3 \)的无三角形Gorenstein图。

更新日期:2020-08-28
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