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 ω(f)=∑u∈V(D)f(u) , the twin signed double Roman domination number γ∗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 γ∗sdR(D) .
