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Keywords
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twin Roman dominating function, twin Roman domination number, Roman dominating
function, Roman domination number, digraph
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Abstract
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Let D be a finite and simple digraph with vertex set V.D/. A twin Roman dominating
function (TRDF) on D is a labeling f W V.D/ ! f0; 1;2g such that every vertex with label 0
has a in-neighbor and out-neighbor with label 2. The weight of a TRDF f is the value !.f / D Pv2V.D/ f .v/. The twin Roman domination number of a digraph D, denoted by R .D/, equals
the minimum weight of a TRDF on D. In this paper we initiate the study of the twin Roman
domination number in digraphs. In particular, we present sharp bounds for R .D/ and determine
the exact value of the twin Roman domination number for some classes of digraphs.
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