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Let Formula: see text be a commutative ring with unity. The prime ideal sum graph of the ring Formula: see text is the simple undirected graph whose vertex set is the set of all nonzero proper ideals of Formula: see text and two distinct vertices Formula: see text, Formula: see text are adjacent if and only if Formula: see text is a prime ideal of Formula: see text. In this paper, we characterize all commutative Artinian rings whose prime ideal sum graphs are line graphs. Finally, we give a description of all commutative Artinian rings whose prime ideal sum graph is the complement of a line graph.
Mathil et al. (Sat,) studied this question.
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