Abstract This paper resolves the previously open problem of determining the metric dimension of the zero-divisor graph (R) for the Boolean ring R = (Z₂) ⁿ. The unique structure of this graph, characterised by its diameter of 3 and lack of common neighbours, has hindered all standard approaches. We introduce a novel combinatorial method that constructs an explicit resolving set. Consequently, we provide a precise formula for ₘ ( ( (Z₂) ⁿ) ), closing a notable gap in the literature on metric dimensions of zero-divisor graphs. As an application, we compute the metric dimension of a zero-divisor graph of a ring with a Boolean factor.
HOSSEINI et al. (Tue,) studied this question.