In this paper, we give a lower bound of the number of maximal independent sets in a graph G in terms of the Castelnuovo–Mumford regularity of its edge ideal. We also find two classes of graphs achieving this minimum value.

中文翻译：

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图的最大独立集和规律性

在本文中，我们给出了图中最大独立集数的下界G就其边缘理想的 Castelnuovo-Mumford 规律而言。我们还发现有两类图表达到了这个最小值。