Intersection Graph of Graded ideals
Abstract
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 GrG(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 Z2-graded idealization, and we deal with intersection graph of graded ideals when the grading group is an ordered groups.
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