The signed total Roman domatic number of a digraph

Let \(D\) be a finite and simple digraph with vertex set \(V(D)\). A signed total Roman dominating function on the digraph \(D\) is a function \(f : V(D)\longrightarrow{-1,1,2}\) \(\sum_{u\in N-(v)} f(u)\ge 1\) for every \(v\in V(D)\), where \(N^{-}(v)\) consists of all inner neighbors of \(v\) for dominating function on \(D\) with the property that \(\sum_{d}^{i=1}f_i(v)\le 1\) for each \(v \in V (D)\) is called a signed total roman dominating family (of functions) on \(D\). The maximum number of functions in a signed total roman dominating family on \(D\)is the signed total Roman domatic number of \(D\). denoted by \(d_{stR}(D)\). In addition, we determine the signed total Roman domatic number of some digraphs. Some of our results are extensions of well-known properties of the signed total Roman domatic of graphs.