Laplacian Eigenvalues of Threshold Graphs

Part of the Universitext book series (UTX)

Threshold graphs have an interesting structure and they arise in many areas.We will be particularly interested in the Laplacian eigenvalues of threshold graphs. We first review some basic aspects of the theory of majorization.


Degree Sequence Stochastic Matrix Recursive Procedure Multilinear Algebra Spectral Theorem 
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References and Further Reading

  1. 1.
    R. Grone and R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discrete Math., 7(2):221–229 (1994).CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    R. Grone and R. Merris, Indecomposable Laplacian integral graphs, Linear Algebra Appl., 7:1565–1570 (2008).CrossRefMathSciNetGoogle Scholar
  3. 3.
    N.V.R. Mahadev and U.N. Peled, Threshold Graphs and Related Topics, Annals of Discrete Mathematics, 54, North-Holland Publishing Co., Amsterdam, 1995.Google Scholar
  4. 4.
    A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, Mathematics in Science and Engineering, 143, Academic Press, New York-London, 1979.Google Scholar
  5. 5.
    R. Merris, Degree maximal graphs are Laplacian integral, Linear Algebra Appl., 199:381–389 (1994).CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    W. So, Rank one perturbation and its application to the Laplacian spectrum of a graph, Linear and Multilinear Algebra, 46:193–198 (1999).CrossRefMathSciNetzbMATHGoogle Scholar

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© Hindustan Book Agency (India) 2010

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