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The difference between the domination number and the minus domination number of a cubic graph
Yang, XF; Hou, QB; Huang, XS; Xuan, HN
2003-10-01
发表期刊APPLIED MATHEMATICS LETTERS
卷号16期号:7页码:1089-1093
文章类型Article
摘要The closed neighborhood of a vertex subset S of a graph G=(V, E), denoted as N[S], is defined as the union of S and the set of all the vertices adjacent to some vertex of S. A dominating set of a graph G= (V, E) is defined as a set S of vertices such that N[S]=V. The domination number of a graph G, denoted as gamma(G), is the minimum possible size of a dominating set of G. A minus dominating function on a graph G=(V, E) is a function g:V-->{-1,0,1} such that g(N[v])greater than or equal to1 for all vertices. The weight of a minus dominating function g is defined as g(V)=Sigma(vis an element ofV)g(v). The minus domination number of a graph G, denoted as gamma(-)(G), is the minimum possible weight of a minus dominating function on G. It is well known that gamma(-)(G)less than or equal toy(G). This paper is focused on the difference between gamma(G) and gamma(-)(G) for cubic graphs. We first present a graph-theoretic description of gamma(-)(G). Based on this, we give a necessary and sufficient condition for gamma(G)-gamma(-)(G)greater than or equal tok. Further, we present an infinite family of cubic graphs of order 18k+16 and with gamma(G)-gamma(-)(G)greater than or equal tok. (C)2003 Elsevier Ltd. All rights reserved.
关键词Graph Theory Domination Number Minus Domination Number
WOS标题词Science & Technology ; Physical Sciences
收录类别SCI
语种英语
WOS研究方向Mathematics
WOS类目Mathematics, Applied
WOS记录号WOS:000186310400016
引用统计
被引频次:2[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/9870
专题09年以前成果
作者单位1.Chongqing Univ, Coll Comp Sci, Chongqing 400044, Peoples R China
2.Chongqing Univ, Natl Educ Minist Key Lab Electroopt Tech & Syst, Chongqing 400044, Peoples R China
3.Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100080, Peoples R China
4.Wuyi Univ, Dept Comp Sci, Jiangmen 529020, Guangdong, Peoples R China
推荐引用方式
GB/T 7714
Yang, XF,Hou, QB,Huang, XS,et al. The difference between the domination number and the minus domination number of a cubic graph[J]. APPLIED MATHEMATICS LETTERS,2003,16(7):1089-1093.
APA Yang, XF,Hou, QB,Huang, XS,&Xuan, HN.(2003).The difference between the domination number and the minus domination number of a cubic graph.APPLIED MATHEMATICS LETTERS,16(7),1089-1093.
MLA Yang, XF,et al."The difference between the domination number and the minus domination number of a cubic graph".APPLIED MATHEMATICS LETTERS 16.7(2003):1089-1093.
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