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最大度和次大度相等的双星树由它的Laplacian谱确定 被引量：2

Double-Star Tree with Largest and Second Dergee Equal Determined by its Spectrum
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摘要 哪些图由它的谱确定问题起源于化学.对于该问题特别是"哪些图由它的邻接谱或Laplacian谱确定?"的研究结果目前还不多.本文主要证明了一类最大度和次大度相等的双星树由它的Laplacian谱确定. The question ＂which graphs are determined by their spectra？＂ originates form chemistry. Answering the- question for adjacency of Laplacian matrix.seems out of reach. It is proved that double-starlike tree with the largest degree and the second degree equal is determined by its Laplacian sepctrum.
作者 沈小玲 侯耀平
机构地区 湖南师范大学期刊社 湖南师范大学数学与计算机科学学院
出处 《湖南师范大学自然科学学报》 CAS 北大核心 2007年第3期22-25,共4页 Journal of Natural Science of Hunan Normal University
基金 国家自然科学基金(10471037) 湖南省教育厅科学研究基金资助项目(03B019)
关键词 图谱 同谱图 特征值 双星树 spectrum of a graph cospectral graphs eigenvalue double-star tree
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献16

  • 1BONDY J A,MURTY U S R.Graph theory with applications[M].New York:Macmillan,1976.
  • 2VAN DAM E R,HAEMERS W H.Which graphs are determined by their spectrum?[J].Linear Algebra Appl,2003,373:241-272.
  • 3DOOB M,HAEMERS W H.The complement of the path is determined b its spectrum[J].Linear Algebra Appl,2002,356:57-65.
  • 4SHEN X L,HOU Y P,ZHANG Y P.Graph Zn and some other graphs related to Zn are determined by their spectrum[J].Linear Algebra Appl,2005,405:58-68.
  • 5沈小玲,张远平.星图和最大度为3的似星树由它们的Laplacian谱确定[J].湖南师范大学自然科学学报,2005,28(1):17-20. 被引量：5
  • 6沈小玲,侯耀平.一些由它的Laplacian谱确定的树[J].湖南师范大学自然科学学报,2006,29(1):21-24. 被引量：13
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  • 9OLIVEIRA C S,DE ABREU N M M,JURKIEWILZ S.The characteristic polynomial of the Laplacian of graphs in (a,b)-linear classes[J].Linear Algebra Appl,2002,356:113-121.
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二级参考文献15

  • 1沈小玲,张远平.星图和最大度为3的似星树由它们的Laplacian谱确定[J].湖南师范大学自然科学学报,2005,28(1):17-20. 被引量：5
  • 2BONDY J A,MURTY U S R.Graph theory with applications[M].LTD:The MacMillan Press,1976.
  • 3VAN DAM E R,HAEMERS W H.Which graphs are determined by their spectrum[J].Linear Algebra Appl,2003,373:241-272.
  • 4DOOB M,HAEMERS W H.The complement of the path is determined by its spectrum[J].Linear Algebra Appl,2002,356:57-65.
  • 5CVETKOVI C' D M.Graphs and their speir spectra[J].Univ Beograd Publ Elektrotehn Fak Ser Mat Fiz,1971,354-356:1-50.
  • 6WATANABE M.SCHWENK A J.Integral starlike trees[J].Austral Math Soc,1979,28(A):120-128.
  • 7OLIVEIRA C S,DE N M M ABRER,JURKIEWILZ S.The characteristic polynomial of the Laplacian of graphs in (a,b)-linear classes[J].Linear Algebra Appl,2002,356:113-121.
  • 8KELMANS A K.The number of trees of a graph I[J].Automati Telemah(Automat.Remote Control),1965,26:2 154-2 204.
  • 9KELMANS A K.The number of trees of a graph I[J].Automati Telemah(Automat.Remote Control),1966,27:56-65.
  • 10KELMANS A K.Characteristic polynomial and the number of spanning trees of graphs snd their optimization,lectrures at the All-union workshop on Graph Theory[M].LTD:the Vaivary,Latviiskiy Gos Universitet press,1972.

共引文献14

同被引文献23

  • 1苏晓艳.图W由它的Laplacian谱确定[J].青海师范大学学报（自然科学版）,2009,25(2):19-21. 被引量：1
  • 2沈小玲,侯耀平.一些由它的Laplacian谱确定的树[J].湖南师范大学自然科学学报,2006,29(1):21-24. 被引量：13
  • 3Schwenk J. Almost all trees are cospectral[C]//Harary F. New Directions in the Theory of Graphs. New York:Academic Press,1973.
  • 4Godsil C, Mckay B. Some computational results on the spectral of graphs[ C]//Proceedings of the Fourth Australian Conference on Combinatin Mathematics Adelaide. Lecture Notes in Mathematics. Berlin:Springer- Verlag, 1976.
  • 5Mckay B. On the spectra characterisation of trees[ J]. Ars Combin, 1979,3:219 -232.
  • 6Dam E V, Haemers W H. Which graphs are determined by their spectrum? [ J]. Linear Algebra and Its Applications,2003,373 : 241 -272.
  • 7Shen Xiao- ling, Hou Yao- ping, Zhang Yuan- ping. Graph and some graphs related to are determined by their speetrum[J]. Linear Algebra and Its Applications ,2005,404:58 -68.
  • 8Wang W, Xu C X. Note the T - shape tree is determined by its Laplacian spectrum [ J ]. Linear Algebra and Its Applications, 2006,419(1) :78 -81.
  • 9Liu Xiao- gang, Zhang Yuan- ping, Lu Peng- li. One special double starlike graph is determined by its Laplacian spectrum[ J]. Appl Math Left,2009,22 (4) :435 - 438.
  • 10Cvetkovic D, Doob M, Sachs H. Spectra of Graphs :Theory and Application[ M]. San Diego:Academic Press, 1995.

引证文献2

二级引证文献6

湖南师范大学自然科学学报
2007年 第3期

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