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

Abstract

In this paper, the generalized blow-up of a Boolean lattice $L\cong {\text{2}}^n$ using finite chains is introduced. Also, we compute the strong metric dimension of the zero-divisor graph of the blow-up of a Boolean lattice. These results are applied to calculate the strong metric dimension of the comaximal graph, the comaximal ideal graph, the zero-divisor graph of a reduced ring, and the component graph of a vector space.