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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109346

    Authors: Sheikholeslami, Seyed Mahmoud;Dehgardi, Nasrin;Volkmann, Lutz;Meierling, Dirk
    Keywords: Roman dominating function;Roman domination number;Roman bondage number;digraph
    Date: 2016-12
    Issue Date: 2017-01-17 09:19:46 (UTC+8)
    Publisher: 淡江大學出版中心
    Abstract: Let D=(V,A)D=(V,A) be a finite and simple digraph. A Roman dominating function on DD is a labeling f:V(D)→{0,1,2}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 ff is the value ω(f)=∑v∈Vf(v)ω(f)=∑v∈Vf(v). The minimum weight of a Roman dominating function on a digraph DD is called the Roman domination number, denoted by γR(D)γR(D). The Roman bondage number bR(D)bR(D) of a digraph DD with maximum out-degree at least two is the minimum cardinality of all sets A′⊆AA′⊆A for which γR(D−A′)>γR(D)γR(D−A′)>γR(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.
    Relation: Tamkang Journal of Mathematics 47(4), pp.421-431
    DOI: 10.5556/j.tkjm.47.2016.2100
    Appears in Collections:[淡江數學期刊] 第47卷第4期

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