The metric dimension of annihilator graphs of commutative rings

摘要

Let R be a commutative ring with nonzero identity. The annihilator graph of R, denoted by AG(R), is the (undirected) graph whose vertex set is the set of all nonzero zerodivisors of R and two distinct vertices x and y are adjacent if and only if ann (R)(xy) not equal ann (R)(x) U ann (R)(y). 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.