THE ROMAN BONDAGE NUMBER OF A DIGRAPH

N. Dehgardi ； D. Meierling ； S. M. Sheikholeslami ； L. Volkmann

《Tamkang Journal of Mathematics》 47卷4期 (2016/12) Pp. 421-432

https://doi.org/10.5556/j.tkjm.47.2016.2100

並列摘要

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 ω( f ) =Σ_(v∈V) f (v). The minimum weight of a Roman dominating function on a digraph D is called the Roman domination number, denoted by γ_R(D). The Roman bondage number b_R(D) of a digraph D with maximum out-degree at least two is the minimum cardinality of all sets A' ⊆ A for which γ_R (D-A')＞ γ_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.

並列關鍵字

Roman dominating function ； Roman domination number ； Roman bondage number ； digraph