Intersection graphs of graded ideals of graded rings

Abstract

<abstract><p>In this article, we introduce and study the intersection graph of graded ideals of a graded ring. The intersection graph of $ G- $graded ideals of a graded ring $ R $, denoted by $ Gr_G(R) $, is undirected simple graph defined on the set of nontrivial graded left ideals of $ R $, such that two left ideals are adjacent if their intersection is not trivial. We study properties for these graphs such as connectivity, regularity, completeness, domination numbers, and girth. We also present several results on the intersection graphs related to faithful grading, strong grading, and graded idealization.</p></abstract>