• DocumentCode
    2785652
  • Title

    A note on multiplicity of the Laplacian eigenvalue of trees

  • Author

    Xu, Zhenye ; Yang, Chun

  • Author_Institution
    Sch. of Appl. Math., Univ. of Electron. Sci. & Technol. of China, Chengdu, China
  • fYear
    2009
  • fDate
    23-25 Oct. 2009
  • Firstpage
    77
  • Lastpage
    78
  • Abstract
    Considering the multiplicity mT(¿) of eigenvalue ¿ (which equals 1) of Laplacian matrix of all trees, we get three results: When mT(1) equals n-2, the tree is unique, that is star graph K1, n-1; (ii) there exists no trees satisfying mT(1) equals n-3; (iii) When mT(1) equals n-4, this kind of trees are divided into two types. According to the process of proving, we devise a method to construct trees on some desired properties, which have practical value.
  • Keywords
    eigenvalues and eigenfunctions; trees (mathematics); Laplacian matrix; eigenvalue multiplicity; star graph; trees; Concrete; Eigenvalues and eigenfunctions; Laplace equations; Polynomials; Symmetric matrices; Tree graphs; Tree; eigenvalue(s); multiplicity; star graph;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Apperceiving Computing and Intelligence Analysis, 2009. ICACIA 2009. International Conference on
  • Conference_Location
    Chengdu
  • Print_ISBN
    978-1-4244-5204-0
  • Electronic_ISBN
    978-1-4244-5206-4
  • Type

    conf

  • DOI
    10.1109/ICACIA.2009.5361147
  • Filename
    5361147
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2785652