Abstract
Let [Formula: see text] be a commutative ring with identity. The essential ideal graph of [Formula: see text], denoted by [Formula: see text], is a graph whose vertex set is the set of all nonzero proper ideals of [Formula: see text] and two vertices [Formula: see text] and [Formula: see text] are adjacent whenever [Formula: see text] is an essential ideal. In this paper, we initiate the study of the essential ideal graph of a commutative ring and we investigate its properties.
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