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Abstract
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.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) ! f1; 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.
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