论文标题
封闭的邻里理想
Closed neighborhood ideal of a graph
论文作者
论文摘要
我们介绍了一个与有限简单图相关的无方形单体理想家族，它们的单元发电机对应于底层图的顶点的封闭邻居。任何这样的理想称为图表的封闭邻居理想。我们研究了这些理想的一些代数不变性，例如Castelnuovo-Mumford的规律性和投影维度，并在图形不变的方面对这些不变性介绍了一些组合描述。
We introduce a family of squarefree monomial ideals associated to finite simple graphs, whose monomial generators correspond to closed neighborhood of vertices of the underlying graph. Any such ideal is called the closed neighborhood ideal of the graph. We study some algebraic invariants of these ideals like Castelnuovo-Mumford regularity and projective dimension and present some combinatorial descriptions for these invariants in terms of graph invariants.
