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树的最大特征值的序 被引量：2

Ordering Trees by Their Largest Eigenvalues
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摘要 设Tn为n个顶点的树的集合,Hofmeister M.对Tn中的树的最大特征值进行排序,给出了第1至第5位的序;CHANG An又给出了第6至第8位的序.讨论了树的最大特征值,确定了第9位的值及对应的树. The set of trees with n vertices is denoted by Tn. Hofmeister has determined the first five values of the largest eigenvalue of trees in Tn and the corresponding trees for these values. Inother words, an order of the first five trees in Tn by their largest eigenvalues has been given.Chang An has determined the sixth to eighth trees in the above ordering. In this paper, the order to the ninth tree is extended.
作者 梁修东
机构地区 江南大学理学院
出处 《江南大学学报（自然科学版）》 CAS 2007年第5期627-630,共4页 Joural of Jiangnan University (Natural Science Edition)　
关键词 树 特征多项式 特征值 上界 tree characteristic polynomial eigenvalue upper bound
分类号 O157 [理学—基础数学]
  • 相关文献

参考文献7

  • 1Hofmeister M.On the two largest eigenvalues of trees[J].Linear Algebra Appl,1997,260:43-59.
  • 2CHANG An,HUANG Qiong-xiang.Order trees by their largest eigenvalues[J].Linear Algebra Appl,2003,370:175-184.
  • 3Cvetkovic D M,Doob M,Sachs H.Spectra of Graphs-Theory and Application[M].New York:Academic Press,1980.
  • 4李乔 冯克勤.论图的最大特征根[J].应用数学学报,1979,2(2):167-175.
  • 5GUO J M,TAN S W.On the spectral radius of trees[J].Linear Algebra Appl,2001,329:1-8.
  • 6GUO Ji-ming,SHAO Jia-yu.On the spectral radius of trees with fixed diameter[J].Linear Algebra Appl,2006,413:131-147.
  • 7谭尚旺,郭纪明.树的最大特征值[J].石油大学学报（自然科学版）,2002,26(6):113-117. 被引量：6

二级参考文献6

  • 1HOFMEISTER M. On the two largest eigenvalues[J]. Linear Algebra Appl, 1997,260:43-59.
  • 2XU G H. On the spectral radius of trees with perfect matchings[A]. Combinatorices and Graph Theorey[C]. World Scientific, Singapore,1997.
  • 3GUO J M, TAN S W. On the spectrual radius of trees[J]. Linear Algebra Appl, 2001,329:1-8.
  • 4CVETKOVIC D M, DOOB M and SACHS H. Spectra of Graphs[M]. New York:Academic Press, 1980.
  • 5李乔 冯克勤.论图的最大特征值.应用数学学报,1979,2(2):167-167.
  • 6常安.完美匹配树的次大和次小的最大特征值[J].高校应用数学学报（A辑）,1999,14A(4):397-403. 被引量：2

共引文献26

同被引文献14

  • 1Bondy J A,Murty U S R.Graph Theory With Applications[M].New York:London and Elservier,1976.
  • 2Norman Biggs.Algebraic Graph Theory[M].Cambridge:Cambridge University Press,1993.
  • 3Hofmeister M.On the two largest eigenvalues of trees[J].Linear Algebra and its Applications,1997,260:43-59.
  • 4An Chang,Huang Qiongxiang.Ordering trees by their largest eigenvalues[J].Linear Algebra and its Applications,2003,370:175-184.
  • 5Shao J Y.Bounds on the Kth eignevalue of trees and forests[J].Linear Algebra and its Applications,1991,149:19-34.
  • 6Cvetkovic D,Doob M,Sachs H.Spectra of Graph-Theory and Application[M].New York:Academic Press,1980.
  • 7An Chang.On the largest eigenvalue of a tree with perfect matchings[J].Discrete Mathematics,2003,269:45-63.
  • 8I J. A. Bondy, U. S. R. Murty. Graph Theory with Applications[ M]. New York:London and Elservier, 1976.
  • 9R.J. Wilson. Introduction to graph theory [ M ]. Oliver and Boyd, Edinburgh,1972.
  • 10M. Hofmeister. On the two largest eigenvalues of trees, Linear Algebra and its Applications[J]. 1997,260.

引证文献2

江南大学学报（自然科学版）
2007年 第5期

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