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A three-valued function $fV\to \{-1,0,1\}$ defined on the vertices of a graph $G=(V,E)$ is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every $v\in V$, $f\left(N\right(v\left)\right)\ge 1$, where $N\left(v\right)$ consists of every vertex adjacent to $v$. The weight of an MTDF is $f\left(V\right)=\sum f\left(v\right)$, over all vertices $v\in V$. The minus total domination number of a graph $G$, denoted ${\gamma }_t^{-}\left(G\right)$, equals the minimum weight of an MTDF of $G$. In this paper, we discuss some properties of minus total domination on a graph $G$ and obtain...