Resolvability in complement of the intersection graph of annihilator submodules of a module

Abstract

Let $R$ be a commutative ring and $M$ be an $R$-module. The intersection graph of annihilatorsubmodules of $M$, denoted by ${GA(M)}$, is a simple undirected graph whose vertices are the classes of elements of $Z(M)setminus {rm Ann}_R(M)$ and two distinct classes $[a]$ and$[b]$ are adjacent if and only if ${rm Ann}_M(a)cap {rm Ann}_M(b)not=0$. In this paper, we studythe diameter and girth of $overline{GA(M)}$. Furthermore, we calculate the domination number,metric dimension, adjacency metric dimension and local metric dimension of $overline{GA(M)}$.