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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
total Roman dominating function (TSTRDF) 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) (respectively N+(v)) consists of all in-neighbors
(respectively out-neighbors) of v, and (ii) every vertex u for which f(u) = −1 has an
in-neighbor v and an out-neighbor w with f(v) = f(w) = 2. The weight of an TSTRDF
f is ω(f) = Pv∈V (D) f(v). The twin signed total Roman domination number γ∗
stR(D)
of D is the minimum weight of an TSTRDF on D. In this paper, we initiate the study
of twin signed total Roman domination in digraphs and we present some sharp bounds
on γ∗
stR(D). In addition, we determine the twin signed Roman domination number of
some classes of digraphs.
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