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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 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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