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Abstract
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Let D be a nite 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) ! f1; 1; 2g satisfying the conditions that (i)
P
x2N(v) f(x) 1
and
P
x2N+(v) f(x) 1 for each v 2 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 ff1; f2; : : : ; fdg
oPf distinct twin signed total Roman dominating functions on D with the property that d
i=1 fi(v) 1 for each v 2 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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