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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
Source PublicationAPPLIED MATHEMATICS LETTERS
2003-10-01
Volume16Issue:7Pages:1089-1093
SubtypeArticle
AbstractThe 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.
KeywordGraph Theory Domination Number Minus Domination Number
WOS HeadingsScience & Technology ; Physical Sciences
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000186310400016
Citation statistics
Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9870
Collection09年以前成果
Affiliation1.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
Recommended Citation
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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