Twin signed double Roman domination numbers in directed graphs

Let D = (V, A) be a finite simple directed graph (shortly digraph). A function f : V ->{-1, 1, 2, 3} is called a twin signed double Roman dominating function (TSDRDF) if (i) every vertex v with f(v) = - 1 has at least two in-neighbor assigned a 2 or at least an in-neighbor w with f(w) = 3, also at least two out-neighbor assigned a 2 or at least an out-neighbor w with f(w) = 3 (ii) every vertex v with f(v) = 1 is adjacent to at least an in-neighbor and an out-neighbor w with f(w) >= 2 and (iii) f(N-[v]) >= 1 and f(N+[v]) >= 1 hold for any vertex v. The weight of a TSDRDF f is w(f) =Sigma(u is an element of v) ((D)) f(u), the twin signed double Roman domination number gamma*(sdR) (D) of D is the minimum weight of a TSDRDF on D. In this paper, we initiate the study of twin signed double Roman domination in digraphs and we present some bounds for gamma*(sdR) (D).