论文标题
分级理想的交点图
Intersection Graph of Graded ideals
论文作者
论文摘要
在本文中，我们介绍并研究了分级环的分级理想的交点图。 $ g- $分级的理想的交点图（r，g）$是一个简单的图形，由$ gr_g（r）$表示，如果没有微不足道的相交，它们的顶点是非平凡的分级理想，两个理想是相邻的。我们研究这些图形的图形性能，例如连通性，规律性，完整性，统治数和周长。还讨论了这些相交的图表，以忠实，强大和最初的强大等级。此外，我们研究了$ \ mathbb {z} _2- $分级的理想化的相交图，并且当分级组是有序组时，我们处理分级理想的相交图。
In this article we introduce and study the intersection graph of graded ideals of graded rings. The intersection graph of $G-$graded ideals of a graded ring $(R,G)$ is a simple graph, denoted by $Gr_G(R)$, whose vertices are the nontrivial graded ideals and two ideals are adjacent if they are not trivially intersected. We study graphical properties for these graphs such as connectivity, regularity, completeness, domination numbers, and girth. These intersection graphs for faithful, strong, and first strong gradings are also discussed. In addition, we investigate intersection graphs of $\mathbb{Z}_2-$graded idealization, and we deal with intersection graph of graded ideals when the grading group is an ordered groups.
