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Abstract
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Let D be a finite simple digraph with vertex set V (D) and arc set A(D). A
twin signed Roman dominating function (TSRDF) on the digraph D is a function f :
V (D)→{−1,1,2} satisfying the conditions that (i) Px∈N−[v] f (x) ≥ 1 and Px∈N+[v] f (x) ≥ 1
for each v ∈ V (D), where N−[v] (resp. N+[v]) consists of v and all in-neighbors (resp.
out-neighbors) of v, and (ii) every vertex u for which f (u) = −1 has an in-neighbor v
and an out-neighbor w for which f (v) = f (w) = 2. The weight of an TSRDF f is !( f ) =
Pv∈V (D) f (v). The twin signed Roman domination number °∗sR(D) of D is the minimum
weight of an TSRDF on D. In this paper, we initiate the study of twin signed Roman
domination in digraphs and we present some sharp bounds on °∗s R(D). In addition, we
determine the twin signed Roman domination number of some classes of digraphs.
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