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

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=۰. 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)}.

Keywords:

Prime submodule‎ , ‎Annihilator submodule‎ , ‎Intersection graph