Domination Number of Total Graph of Module

Let rr be a commutative ring and mm be an rr-module with t(m) as subset, the set of torsion elements. the total graph of the module denoted by t(γ(m)), is the (undirected) graph with all elements of mm as vertices, and for distinct elements n,m∈mn,m∈m, the vertices nn and mm are adjacent if and only if n+m∈t(m)n+m∈t(m). in this paper we study the domination number of t(γ(m))t(γ(m)) and investigate the necessary conditions for being zn as module over zm and we find the domination number of t(γ(zn)).