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图的符号树控制数 被引量:1

On Signed Tree Domination Numbers of Graphs
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摘要 引入了图的符号树控制的概念,给出一个连通图G的符号树控制数γ′T(G)的一个上界和一个下界,说明了这两个界限均是最好可能的,并确定几类特殊图的符号树控制数,这包括了圈、轮图、完全图和完全二部图. In this paper we introduce the concept of signed tree domination in graphs, we obtain a upper bound and a lower bound of signed tree domination numbers for general graphs G, and show that the two bounds are best possible. In addition, we determine the signed tree domination numbers for some special classes of graphs G, including cycles, wheels, complete graphs and complete bipartite graphs.
出处 《华东交通大学学报》 2008年第2期56-58,共3页 Journal of East China Jiaotong University
基金 国家自然科学基金项目(10661007) 江西省自然科学基金项目(2007GZS0715)
关键词 符号树控制函数 符号树控制数 轮图 完全图 完全二部图 signed tree dominating function, signed tree domination number, cycles, wheels, complete graphs, complete bi-partite 1~7"aphs
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参考文献8

  • 1Bondy J A, Murty V S R. Graph Theory with Applications[ M]. New Tork: Elsevier, 1976.
  • 2Cockayne E J, Mynhart C M. On a generalization of signed domination functions of graphs[ J], Ars. Combin. 1996, (43) :235 - 245.
  • 3Haynes T W, Hedetniemi S T, Slater P J. Domination in graphs [M],New York:Marcel Dekker, INC, 1998.
  • 4T. W. Haynes, S. T. Hedemiemi, and P. J. Slater, Fundamental of domination in graphs[ M], New York: Marcel Dekker, INC 1998.
  • 5Baogen. Xu, On signed edge domination numbers of graphs[J] Discrete Math.2001, (239) : 179 - 189.
  • 6Baogen. Xu, On edge domination numbers of graphs[J]. Discrete Math.2005, (294) :311 - 316.
  • 7Baogen. Xu,Two classes of edge domination in graphs[J]. Discrete Appl. Math. 2006, (154) : 1541 - 1546.
  • 8徐保根,周尚超.图与补图的符号圈控制数[J].江西师范大学学报(自然科学版),2006,30(3):249-251. 被引量:9

二级参考文献6

  • 1徐保根.图的符号圈控制[J].华东交通大学学报,2005,22(5):135-137. 被引量:4
  • 2F哈拉里.图论[M].上海:上海科学技术出版社,1980..
  • 3Haynes T W,Hedetniemi S T,Slater P J.Domination in graphs[M].New York:Marcel Dekker,INC,1998.
  • 4Haynes T W,Hedetniemi S T,Slater P J.Fundamentals of domination in graphs[M].New York:Marcel Dekker,INC,1998.
  • 5Xu Bao-gen.On signed edge domination numbers of graphs[J].Discrete Math,2001,239:179-189.
  • 6Xu Bao-gen.On edge domination numbers of graphs[J].Discrete Math,2005,294:311-316.

共引文献8

同被引文献10

  • 1徐保根.图的符号圈控制[J].华东交通大学学报,2005,22(5):135-137. 被引量:4
  • 2徐保根,周尚超.图与补图的符号圈控制数[J].江西师范大学学报(自然科学版),2006,30(3):249-251. 被引量:9
  • 3徐保根,周尚超.关于图的减边控制[J].江西师范大学学报(自然科学版),2007,31(1):21-24. 被引量:15
  • 4Bondy J A,Murty V S R.Graph theory with applications [M] .Amsterdam:Elsevier, 1976.
  • 5Cockayne E J, Mynhart C M. On a generalization of signed domination functions of graphs [ J]. Ars Combin, 1996,43:235-245.
  • 6Haynes T W, Hedemiemi S T,Slater P J. Domination in graphs [M].New York:Marcel Dekker, 1998.
  • 7Xu Bao-gen, Cockayne E J, Haynes T W, et al. Extremal graphs for inequalities involving domination parameters [ J]. Discrete Math, 2000,216:1-10.
  • 8Zhang Z,Xu Bao-gen,Li Y,et al.A note on the lower bounds of signed domination number of a graph [J] .Discrete Math, 1999, 195: 295-298.
  • 9Xu Bao-gen. On signed edge domination numbers of graphs [ J]. Discrete Math,2001,239:179-189.
  • 10徐保根.On Minus Domination and Signed Domination in Graphs[J].Journal of Mathematical Research and Exposition,2003,23(4):586-590. 被引量:21

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