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

TL;DR

This paper investigates the strong metric dimension of various graph classes derived from algebraic structures, providing explicit calculations for the complement of the zero-divisor graph of a lattice and related graphs.

Contribution

It introduces new formulas for the strong metric dimension of these graphs, expanding understanding of their metric properties in algebraic contexts.

Findings

Strong metric dimension of the complement of zero-divisor graph of a Boolean lattice is computed.

Explicit formulas for total, maximal, and intersection graphs of ideals are provided.

Results apply to graphs associated with reduced rings and vector spaces.

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.