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Abstract
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Abstract Let D be a finite and simple digraph with vertex set V(D) and arc set
A(D). A signed Roman dominating function (SRDF) on the digraph D is a function
f : V(D) → {−1, 1, 2} satisfying the conditions that (i)x∈N−[v] f (x) ≥ 1 for each
v ∈ V(D), where N−[v] consists of v and all in-neighbors of v, and (ii) every vertex
u for which f (u) = −1 has an in-neighbor v for which f (v) = 2. The weight of an
SRDF f is w( f ) = v∈V(D) f (v). The signed Roman domination number γsR(D)
of D is the minimum weight of an SRDF on D. In this paper we initiate the study of
the signed Roman domination number of digraphs, and we present different bounds
on γsR(D). In addition, we determine the signed Roman domination number of some
classes of digraphs. Some of our results are extensions of well-known properties of
the signed Roman domination number γsR(G) of graphs G.
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