The metric dimension of annihilator graphs of commutative rings

Abstract

Let [Formula: see text] be a commutative ring with nonzero identity. The annihilator graph of [Formula: see text], denoted by [Formula: see text], is the (undirected) graph whose vertex set is the set of all nonzero zero-divisors of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we study the metric dimension of annihilator graphs associated with commutative rings and some metric dimension formulae for annihilator graphs are given.