Strong resolving graph and strong metric dimension of a compressed zero divisor graph

Let [Formula: see text] be a commutative ring with [Formula: see text] and [Formula: see text] be the set of zero-divisors of [Formula: see text]. The relation on [Formula: see text] given by [Formula: see text] if and only if [Formula: see text] is an equivalence relation, where [Formula: see text]. The compressed zero divisor graph [Formula: see text] of [Formula: see text] is a simple graph whose vertex set is the set of all equivalence [Formula: see text]-classes and two distinct [Formula: see text]-classes [Formula: see text] and [Formula: see text] are adjacent if [Formula: see text]. In this paper, the structure of strong resolving graph of [Formula: see text] is completely determined. Using the structure, we calculate the strong metric dimension of [Formula: see text].