مشخصات پژوهش

.Abstract. Let D = (V;A) be a nite simple digraph. A signed double Roman dominating function (SDRD-function) on the digraph D is a function f : V (D) ! f􀀀1; 1; 2; 3g satisfying the following conditions: (i) P x2N􀀀[v] f(x)  1 for each v 2 V (D), where N􀀀[v] consist of v and all in-neighbors of v, and (ii) if f(v) = 􀀀1, then the vertex v must have at least two in-neighbors assigned 2 under f or one in-neighbor assigned 3, while if f(v) = 1, then the vertex v must have at least one in-neighbor assigned 2 or 3. The weight of a SDRD-function f is the value P x2V (D) f(x). The signed double Roman domination number (SDRD-number) sdR(D) of a digraph D is the minimum weight of a SDRD-function on D. In this paper we study the SDRD-number of digraphs, and we present lower and upper bounds for sdR(D) in terms of the order, maximum degree and chromatic number of a digraph. In addition, we determine the SDRD-number of some classes of digraphs.