On the strong metric dimension of the complement of the zero-divisor graph of a lattice

Abstract: In this paper, we compute the strong metric dimension of the complement of the zero-divisor graph of the blow-up of a Boolean lattice. Using these results, we calculate the strong metric dimension of the total graph, the maximal graph, the intersection graph of ideals, the complement of the zero-divisor graph of a reduced ring, and the component graph of a vector space.