On line upper ideal relation graphs of rings

The upper ideal relation graph ΓU(R) of a commutative ring R with unity is a simple undirected graph with the set of all non-unit elements of R as a vertex set and two vertices x, y are adjacent if and only if the principal ideals $(x)$ and $(y)$ are contained in the principal ideal $(z)$ for some non-unit element z∈ R. This manuscript characterizes all the Artinian rings R such that the graph ΓU(R) is a line graph. Moreover, all the Artinian rings R for which ΓU(R) is the complement of a line graph have been described.