KMS Of Academy of mathematics and systems sciences, CAS
| Roman domination in a tree | |
| Song, Xiaoxin1,2; Shang, Weiping3 | |
| 2011 | |
| 发表期刊 | ARS COMBINATORIA
 |
| ISSN | 0381-7032 |
| 卷号 | 98页码:73-82 |
| 摘要 | A Roman dominating function on a graph G = (V, E) is a function f : V -> {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V) = Sigma(u is an element of V) f (u). The minimum weight of a Roman dominating function on a graph G, denoted by gamma R(G), is called the Roman domination number of G. In [E.J. Cockayne, P.A. Dreyer, Jr., S.M. Hedetniemi, S.T. Hedetniemi, Roman domination in graphs, Discrete Math. 278(2004) 11-22.], the authors stated a proposition which characterized trees which satisfy gamma R(T) = gamma(T) + 2, where gamma(T) is the domination number of T. The authors thought the proof of the proposition was rather technical and chose to omit it's proof, however, the proposition is actually incorrect. In this paper, we will give a counterexample of this proposition and introduce the correct characterization of a tree T with gamma R(T) = gamma(T) + 2. |
| 关键词 | Roman dominating function Roman domination number Domination number healthy spider wounded spider |
| 语种 | 英语 |
| 资助项目 | N.S.F. of education Department of Henan Province[200510475038] |
| WOS研究方向 | Mathematics |
| WOS类目 | Mathematics |
| WOS记录号 | WOS:000286533200007 |
| 出版者 | CHARLES BABBAGE RES CTR |
| 引用统计 | |
| 文献类型 | 期刊论文 |
| 条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/13145 |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Song, Xiaoxin |
| 作者单位 | 1.Henan Univ, Coll Math & Informat Sci, Kaifeng 475001, Peoples R China 2.Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China 3.Chinese Acad Sci, Inst Appl Maths, Acad Maths & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Song, Xiaoxin,Shang, Weiping. Roman domination in a tree[J]. ARS COMBINATORIA,2011,98:73-82. |
| APA | Song, Xiaoxin,&Shang, Weiping.(2011).Roman domination in a tree.ARS COMBINATORIA,98,73-82. |
| MLA | Song, Xiaoxin,et al."Roman domination in a tree".ARS COMBINATORIA 98(2011):73-82. |
| 条目包含的文件 | 条目无相关文件。 | |||||
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