| 图上Nordhaus-Gaddum型的符号全控制数的界 |
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| 引用本文： | 史伟,康丽英,徐兰栓. 图上Nordhaus-Gaddum型的符号全控制数的界[J]. 运筹学学报, 2008, 12(2): 67-72 |
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| 作者姓名： | 史伟 康丽英 徐兰栓 |
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| 作者单位： | 1. 上海大学数学系,上海,200444
2. 邢台广播电视大学,邢台,050021 |
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| 摘 要： | 函数f:V(G)→{-1,1}称为图G的符号全控制函数,如果对每一个开邻域集上的点的函数值的和都大于等于1.符号全控制函数的权值是指图中所有点的函数值的求和.图的符号全控制数为图中所有符号全控制函数的最小权值.令G表示图G的补图.在该文中,我们研究符号全控制数的Nordhaus-Gaddum型不等式,给出了路与其补图的符号全控制数和的上界,以及图与其补图的符号全控制数和的下界.
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| 关 键 词： | 运筹学 符号全控制函数 Nordhaus-Gaddum型结果 补图 路 Operations research signed total domination nordhaus-gaddum result complement path 符号 全控制数 Graphs Signed Total Domination path lower bound upper bound paper study type results complement signed total domination number minimum weight values open neighborhood defined graph |
Nordhaus-Gaddum Results for Signed Total Domination in Graphs |
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| Shi Wei,Kang Liying,Xu Lanshuan. Nordhaus-Gaddum Results for Signed Total Domination in Graphs[J]. OR Transactions, 2008, 12(2): 67-72 |
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| Authors: | Shi Wei Kang Liying Xu Lanshuan |
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| Abstract: | A function f: V(G)→{-1,1} defined on the vertices of a graph G is a signed total dominating function (STDF) if the sum of its function values over any open neighborhood is at least one. The weight of a STDF is the sum of its function values over all vertices. The signed total domination number of G is the minimum weight of a STDF on G. Let G denote the complement of a graph G. In this paper we study Nordhaus-Gaddum type results for signed total domination number. An upper bound on γ8t(Pn)+γ8t(Pn) for a path Pn and a lower bound on γ8t(G)+γ8t(G) are presented. |
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| Keywords: | Operations research signed total domination nordhaus-gaddum result complement path |
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