Science China Mathematics

, Volume 53, Issue 8, pp 2135–2142 | Cite as

The Laplacian spectral radii of unicyclic and bicyclic graphs with n vertices and k pendant vertices

Articles

Abstract

In this paper, we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices, respectively.

Keywords

Laplacian matrix Laplacian spectral radius unicyclic graph bicyclic graph 

MSC(2000)

05C50 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Anderson W N, Morley T D. Eigenvalues of the Laplacian of a graph. Linear Multilinear Algebra, 1985, 18: 141–145MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Grone R, Merris R. The Laplacian spectrum of graph II. SIAM J Discrete Math, 1994, 7: 221–229MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Guo J M. On the Laplacian spectral radius of a tree. Linear Algebra Appl, 2003, 368: 379–385MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Guo J M. The effect on the Laplacian spectral radius of a graph by adding or grafting edges. Linear Algebra Appl, 2006, 413: 59–71MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Guo J M. The Laplacian spectral radius of a graph under perturbation. Comput Math Appl, 2007, 54: 709–720MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Guo S G. The spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices. Linear Algebra Appl, 2005, 408: 78–85MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gutman I, Vidović D, Stevanović D. Chemical applications of the Laplacian spectrum. VI. On the largest Laplacain eigenvalue of alkanes. J Serb Chem Soc, 2002, 67: 407–413CrossRefGoogle Scholar
  8. 8.
    Hong Y, Zhang X D. Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees. Discrete Math, 2005, 296: 187–197MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Li J S, Zhang X D. On Laplacian eigenvalues of a graph. Linear Algebra Appl, 1998, 285: 305–307MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Merris R. Laplacian matrices of graphs: a survey. Linear Algebra Appl, 1994, 198: 143–176CrossRefMathSciNetGoogle Scholar
  11. 11.
    Merris R. Laplacian graph eigenvectors. Linear Algebra Appl, 1998, 278: 221–236MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Mohar B. The Laplacian spectrum of graphs. Graph Theory, Combinatorics, and Applications, 1991, 2: 871–898MathSciNetGoogle Scholar
  13. 13.
    Pan Y L. Sharp upper bounds for the Laplacian graph eigenvalues. Linear Algebra Appl, 2002, 355: 287–295MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Applied MathematicsChina University of PetroleumDongyingChina

Personalised recommendations