twin signed total roman domatic numbers in digraphs

let d be a finite simple digraph with vertex set v(d) and arc set a(d). a twin signed total roman dominating function (tstrdf) on the digraph d is a function f:v(d)→{−1,1,2} satisfying the conditions that (i) ∑x∈n−(v)f(x)≥1 and ∑x∈n+(v)f(x)≥1 for each v∈v(d), where n−(v) (resp. n+(v)) consists of all in-neighbors (resp. out-neighbors) of v, and (ii) every vertex u for which f(u)=−1 has an in-neighbor v and an out-neighbor w with f(v)=f(w)=2. a set {f1,f2,…,fd} of distinct twin signed total roman dominating functions on d with the property that ∑^d i=1fi(v)≤1 for each v∈v(d), is called a twin signed total roman dominating family (of functions) on d. the maximum number of functions in a twin signed total roman dominating family on d is the twin signed total roman domatic number of d, denoted by d∗str(d). in this paper, we initiate the study of the twin signed total roman domatic number in digraphs and present some sharp bounds on d^∗str(d). in addition, we determine the twin signed total roman domatic number of some classes of digraphs.