MMN-1178
Twin Roman domination number of a digraph
Abstract
Let $D$ be a finite and simple digraph with vertex set $V(D)$. A {\em twin Roman
dominating function} (TRDF) on $D$ is a labeling $f:V (D)\rightarrow \{0, 1, 2\}$
such that every vertex with label 0 has a in-neighbor
and out-neighbor with label 2. The {\em weight} of a TRDF $f$ is
the value $\omega(f)=\sum_{v\in V(D)}f (v)$. The {\em twin Roman
domination number} of a digraph $D$, denoted by $\gamma_R^*(D)$,
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
$\gamma_{R}^*(D)$ and determine the exact value of twin Roman
domination number for some classes of digraphs.
Vol. 17 (2016), No. 1, pp. 3-14
DOI: 10.18514/MMN.2016.1178