SIGNED TOTAL DOUBLE ROMAN DOMINATION NUMBERS IN DIGRAPHS.

Let D = (V, A) be a finite simple digraph. A signed total double Roman dominating function (STDRD-function) on the digraph D is a function ƒ : V (D) → {-1; 1; 2; 3} satisfying the following conditions: (i) Σ_x∈N-(v) ƒ(x) ≥ 1 for each v ∈ V (D), where N^-(v) consist of all in-neighbors of v, and (ii) if ƒ(v) = -1, then the vertex v must have at least two in-neighbors assigned 2 under ƒ or one in-neighbor as igned 3 under ƒ, while if ƒ(v) = 1, then the vertex v must have at least one in-neighbor assigned 2 or 3 under ƒ. The weight of a STDRD-function ƒ is the value ∑_x∈V(D) ƒ(x). The signed total double Roman domination number (STDRD-number) γ_sdR^t(D) of a digraph D is the minimum weight of a STDRD-function on D. In this paper we study the STDRD-number of digraphs, and we present lower and upper bounds for γ_sdR^t(D) in terms of the order, maximum degree and chromatic number of a digraph. In addition, we determine the STDRD-number of some classes of digraphs. [ABSTRACT FROM AUTHOR]