Twin signed Roman domination numbers in directed graphs

Seyed Mahmoud Sheikholeslami, Asghar Bodaghli, Lutz Volkmann
2016 Tamkang Journal of Mathematics  
Let D be a finite simple digraph with vertex set V (D) and arc set A(D). A twin signed Roman dominating function (TSRDF) on the digraph D is a function f : consists of v and 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 for which The twin signed Roman domination number γ * sR (D) of D is the minimum weight of an TSRDF on D. In this paper, we initiate the study of twin signed Roman domination in digraphs and
more » ... n in digraphs and we present some sharp bounds on γ * sR (D). In addition, we determine the twin signed Roman domination number of some classes of digraphs. ) denote the number of in-neighbors (resp. out-neighbors) of v in S. If X ⊆ V (D), then D[X ] is the subdigraph induced by X . If X ⊆ V (D) and v ∈ V (D), then A(X , v) is the set of arcs from
doi:10.5556/j.tkjm.47.2016.2035 fatcat:3fss63b2zbdlfkm4iu7gwy7qsm