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关于图的符号边全控制数 被引量：6

On Signed Edge Total Domination Numbers of Graphs
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摘要 引入了图的符号边全控制的概念,给出了一个连通图G的符号边全控制数γs′t(G)的下限,确定所有n阶树T的最小符号边全控制数,并刻划了满足γs′t(G)=E(G)的所有连通图G,最后还提出了一个关于γs′t(G)上界的猜想. We introduce the concept of signed edge total domination in graphs, obtain a lower bound for the signed edge total domination numbers of graphs, and determine the smallest signed edge total domination number for all tree of order n, and characterize all connected graphs with γ′_st（G）=｜E（G）｜.In addition, we pose a conjecture about the upper bound of γ′_st（G）.
作者 徐保根 李印权
机构地区 华东交通大学数学系
出处 《数学的实践与认识》 CSCD 北大核心 2009年第5期138-144,共7页 Mathematics in Practice and Theory
基金 国家自然科学基金(10661007) 江西省自然科学基金(2007G2S0715)
关键词 符号边全控制函数 符号边全控制数 树 signed edge total domination function signed edge total domination number tree
分类号 O157.5 [理学—基础数学]
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参考文献11

  • 1Bondy J A, Murty V S R. Graph Theory with Applications[M]. Elsevier, Amsterdam,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. Fundamentals of Domination in Graphs[M]. New York, 1998.
  • 4Haynes T W, Hedetniemi S T, Slater P J. Domination in Graphs[M]. New York,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.
  • 8Zhang Z, Baogen Xu, Li Y, Liu L. A note on the lower bounds of signed domination number of a graph[J]. Discrete Math, 1999,195:295-298.
  • 9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
  • 10Baogen Xu, Cockayne E J, Haynes T W, Hedetniemi S T, Zhou S. Extremal graphs for inequalities involving domination parameters [J]. Discrete Math, 2000,216 : 1-10.

二级参考文献8

  • 1DUNBAR J, HEDETNIEMI S, HENNING M A. et al. Minus dominationin graphs [J]. Discrete Math, 1999, 199: 35-47.
  • 2BONDY J A, MURTY V S R. Graph Theory with Applications [M]. Elsevier, Amsterdam, 1976.
  • 3ZHANG Zhong-fu, XU Bao-gen, LI Yin-zhen. et al. A note on the lower bounds of signed domination number of a graph [J]. Discrete Math, 1999, 195: 295-298.
  • 4LEE J, SOHN M Y, KIM H K. A note on graphs with large girth and small minus domination number [J]. Discrete Applied Math, 1999, 91: 299-303.
  • 5CHARTRAND G, LESNIAK L. Graphs & Digraphs [M]. Second ed. Wadsworth & Brooks/Cole, Monterey, 1986.
  • 6XU Bao-gen, COCKAYNE E J, HAYNES T W. et al. Exteremal graphs for inequalities involving domination parameters [J] . Discrete Math, 2000, 216: 1-10.
  • 7XU Bao-gen, ZHOU Shang-chao. Characterization of connected graphs with maximum domination number [J]. J Math Res Exposition, 2000, 4: 523-528.
  • 8XU Bao-gen. On signed edge domination numbers of graphs [J]. Discrete Math, 2001, 239: 179-189.

共引文献21

同被引文献38

引证文献6

二级引证文献17

数学的实践与认识
2009年 第5期

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