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) Px∈N−(v) f(x) ≥ 1 and Px∈N+(v) f(x) ≥ 1 for each v ∈ V (D), where N−(v) (respectively N+(v)) consists of all in-neighbors (respectively 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. The weight of an TSTRDF f is ω(f) = Pv∈V (D) f(v). The twin signed total Roman domination number γ∗ stR(D) of D is the minimum weight of an TSTRDF on D. In this paper, we initiate the study of twin signed total Roman domination in digraphs and we present some sharp bounds on γ∗ stR(D). In addition, we determine the twin signed Roman domination number of some classes of digraphs.