The Laplacian spectral radius of graphs

Jianxi Li; Wai Chee Shiu; An Chang

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 3, page 835-847
  • ISSN: 0011-4642

Abstract

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The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we improve Shi's upper bound for the Laplacian spectral radius of irregular graphs and present some new bounds for the Laplacian spectral radius of some classes of graphs.

How to cite

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Li, Jianxi, Shiu, Wai Chee, and Chang, An. "The Laplacian spectral radius of graphs." Czechoslovak Mathematical Journal 60.3 (2010): 835-847. <http://eudml.org/doc/38044>.

@article{Li2010,
abstract = {The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we improve Shi's upper bound for the Laplacian spectral radius of irregular graphs and present some new bounds for the Laplacian spectral radius of some classes of graphs.},
author = {Li, Jianxi, Shiu, Wai Chee, Chang, An},
journal = {Czechoslovak Mathematical Journal},
keywords = {graph; Laplacian spectral radius; bounds; graph; Laplacian spectral radius; bound},
language = {eng},
number = {3},
pages = {835-847},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Laplacian spectral radius of graphs},
url = {http://eudml.org/doc/38044},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Li, Jianxi
AU - Shiu, Wai Chee
AU - Chang, An
TI - The Laplacian spectral radius of graphs
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 835
EP - 847
AB - The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we improve Shi's upper bound for the Laplacian spectral radius of irregular graphs and present some new bounds for the Laplacian spectral radius of some classes of graphs.
LA - eng
KW - graph; Laplacian spectral radius; bounds; graph; Laplacian spectral radius; bound
UR - http://eudml.org/doc/38044
ER -

References

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  1. Bondy, J., Murty, U., Graph Theory with Applications, MacMillan New York (1976). (1976) MR0411988
  2. Cioabǎ, S., 10.37236/956, Electron. J. Combin. 14, R38 (2007). (2007) MR2320594DOI10.37236/956
  3. Haemers, W., Interlacing eigenvalues and graphs, Linear Algebra Appl. 226-228 (1995), 593-616. (1995) Zbl0831.05044MR1344588
  4. Merris, R., Laplacian matrix of graphs: a survey, Linear Algebra Appl. 197-198 (1994), 143-176. (1994) MR1275613
  5. Liu, B., Shen, J., Wang, X., 10.1016/j.jctb.2007.02.008, J. Combin. Theory Ser. B. 97 (2007), 1010-1018. (2007) Zbl1125.05062MR2354715DOI10.1016/j.jctb.2007.02.008
  6. Mohar, B., Some applications of Laplace eigenvalues of graphs. Notes taken by Martin Juvan, Graph Symmetry: Algebraic Methods and Applications. NATO ASI Ser., Ser. C, Math. Phys. Sci. Vol. 497 G. Hahn et al. Kluwer Academic Publishers Dordrecht (1997), 225-275. (1997) Zbl0883.05096MR1468791
  7. Motzkin, T., Straus, E., 10.4153/CJM-1965-053-6, Canad. J. Math. 17 (1965), 533-540. (1965) Zbl0129.39902MR0175813DOI10.4153/CJM-1965-053-6
  8. Nikiforov, V., Bounds on graph eigenvalues II, Linear Algebra Appl. 427 (2007), 183-189. (2007) Zbl1128.05035MR2351351
  9. Shi, L., 10.1016/j.laa.2006.12.003, Linear Algebra. Appl. 422 (2007), 755-770. (2007) Zbl1113.05065MR2305155DOI10.1016/j.laa.2006.12.003
  10. Stevanovi'c, D., 10.1016/j.jctb.2003.12.002, J. Combin. Theory Ser. B. 91 (2004), 143-146. (2004) MR2047537DOI10.1016/j.jctb.2003.12.002
  11. Zhang, X.-D., Luo, R., The spectral radius of triangle-free graphs, Australas. J. Comb. 26 (2002), 33-39. (2002) Zbl1008.05089MR1918140
  12. Zhang, X.-D., 10.1016/j.laa.2005.03.020, Linear Algebra Appl. 409 (2005), 79-86. (2005) MR2170268DOI10.1016/j.laa.2005.03.020

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