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Abstract
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Let D = (V, A) be a finite and simple digraph. A Roman dominating function on
D is a labeling f : V (D)→{0,1,2} such that every vertex with label 0 has an in-neighbor
with label 2. The weight of an RDF f is the value !( f ) =Pv∈V f (v). The minimum weight
of a Roman dominating function on a digraph D is called the Roman domination number,
denoted by °R(D). The Roman bondage number bR(D) of a digraph D with maximum
out-degree at least two is theminimumcardinality of all sets A′ ⊆ A forwhich °R (D−A′)>
°R(D). In this paper, we initiate the study of the Roman bondage number of a digraph.
We determine the Roman bondage number in several classes of digraphs and give some
sharp bounds.
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