مشخصات پژوهش

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) P x∈N−(v) f(x) ≥ 1 and P 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 P D with the property that d i=1 fi(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.