华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (3): 29-34.

• 应用数学与基础数学 • 上一篇    下一篇

给定最大度的树的代数连通度

顾 磊;袁炜罡;张晓东   

  1. 上海交通大学 数学系, 上海 200240
  • 收稿日期:2010-12-01 修回日期:2011-03-01 出版日期:2011-05-25 发布日期:2011-05-25
  • 通讯作者: 顾磊

Algebraic connectivity of trees with the maximum degree

GU Lei;YUAN Wei-gang; ZHANG Xiao-dong   

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2010-12-01 Revised:2011-03-01 Online:2011-05-25 Published:2011-05-25
  • Contact: GU Lei

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摘要： 研究给定最大度的树在移接变形下的代数连通度的变化. 这些结果可以用来刻画给定最大度和顶点个数的树中具有最小代数连通度的极图, 并且给出了该极图的代数连通度的一个下界.

关键词: 代数连通度, 树, 拉普拉斯矩阵, 最大度, 代数连通度, 树, 拉普拉斯矩阵, 最大度

Abstract: This paper investigated how the algebraic connectivity of trees changes under some graph perturbations. Then these results were used to characterize the extremal tree which has the smallest algebraic connectivity in the set of trees given the number of vertex and the maximum degree.

Key words: tree, Laplacian matrix, maximum degree, algebraic connectivity, tree, Laplacian matrix, maximum degree

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