Abstract
The regular graph of ideals of a commutative ring [Formula: see text], denoted by [Formula: see text], is a graph whose vertex-set is the set of all nontrivial ideals of [Formula: see text] and, for every two distinct vertices [Formula: see text] and [Formula: see text], there is an edge between [Formula: see text] and [Formula: see text], whenever [Formula: see text] contains a nonzero zero-divisor on [Formula: see text] or vice versa. In this paper, we will show that [Formula: see text] is isomorphic to an induced sub-graph of [Formula: see text] which nicely can describe [Formula: see text]. This approach enables us to find the independence number of [Formula: see text] when [Formula: see text] is a reduced ring. Among other things, some basic graph theoretic properties of [Formula: see text] and relevant ring theoretic properties of [Formula: see text] will be studied.
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