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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) P
x∈N−(v)
f(x) ≥ 1
and P
x∈N+(v)
f(x) ≥ 1 for each v ∈ V (D), where N−(v) (resp. N+(v)) consists of 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 with f(v) = f(w) = 2. A set {f1, f2, . . . , fd}
of distinct twin signed total Roman dominating functions on
P
D with the property that
d
i=1 fi(v) ≤ 1 for each v ∈ V (D), is called a twin signed total Roman dominating
family (of functions) on D. The maximum number of functions in a twin signed total
Roman dominating family on D is the twin signed total Roman domatic number of
D, denoted by d
∗
stR(D). In this paper, we initiate the study of the twin signed total
Roman domatic number in digraphs and present some sharp bounds on d
∗
stR(D). In
addition, we determine the twin signed total Roman domatic number of some classes
of digraphs.
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