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 $T(\Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m \in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m \in T(M)$. In this paper we study the domination number of $T(\Gamma(M))$ and investigate the necessary conditions for being $\mathbb{Z}_{n}$ as module over $\mathbb{Z}_{m}$ and we find the domination number of $T(\Gamma(\mathbb{Z}_{n}))$.

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