Principal Intersection Graph of Commutatives Rings

Let \(R\) be a commutative ring. The principal intersection graph of a commutative ring \(R\), noted \(G_{c}(R)\), consists of all proper ideals of \(R\) as vertices. Two distinct vertices \(I\) and \(J\) are adjacent if \(I\cap J \neq 0\) and either \(I\) or \(J\) is a principal (cyclic) ideal. In this paper, we investigate some properties from graph theory of \(G_{c}(R)\) and its algebraic properties where \(R\) is a ring.