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The upper ideal relation graph ₔ (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 ₔ (R) is a line graph. Moreover, all the Artinian rings R for which ₔ (R) is the complement of a line graph have been described.
Shariq et al. (Wed,) studied this question.
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