DOMINATION NUMBER OF TOTAL GRAPH OF MODULE

Let R be a commutative ring and M be an R-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 M as vertices, and for distinct elements n,m∈M, the vertices n and m are adjacent if and only if n∈T(M). In this paper we study the domination number of 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)).