Line graph embedding of co-intersection graph of ideals of commutative rings

This research paper focuses on the co-intersection graph of a commutative ring [Formula: see text]. The co-intersection graph of [Formula: see text] denoted by [Formula: see text] is a simple graph with vertices that are non-trivial ideals of [Formula: see text], and two distinct vertices I and J are adjacent if and only if [Formula: see text]. The primary goal of this study is to characterize Artinian commutative rings [Formula: see text], and determining whether their associated co-intersection graph [Formula: see text] forms a line graph and identifying instances where it becomes the complement of a line graph. Additionally, the article investigates the planarity and outerplanarity of the line graph of the co-intersection graph [Formula: see text]. Finally, the research identifies the genus one of this line graph of co-intersection graph of ideals of a commutative ring.