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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 Publication APPLIED MATHEMATICS LETTERS 2003-10-01 Volume 16Issue:7Pages:1089-1093 Subtype Article Abstract 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. Keyword Graph Theory Domination Number Minus Domination Number WOS Headings Science & Technology ; Physical Sciences Indexed By SCI Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000186310400016 Citation statistics Document Type 期刊论文 Identifier http://ir.ia.ac.cn/handle/173211/9870 Collection 09年以前成果 Affiliation 1.Chongqing Univ, Coll Comp Sci, Chongqing 400044, Peoples R China2.Chongqing Univ, Natl Educ Minist Key Lab Electroopt Tech & Syst, Chongqing 400044, Peoples R China3.Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100080, Peoples R China4.Wuyi Univ, Dept Comp Sci, Jiangmen 529020, Guangdong, Peoples R China Recommended CitationGB/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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