On the multiplicity of Laplacian eigenvalues of graphs

Ji-Ming Guo; Lin Feng; Jiong-Ming Zhang

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 3, page 689-698
  • ISSN: 0011-4642

Abstract

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In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered.

How to cite

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Guo, Ji-Ming, Feng, Lin, and Zhang, Jiong-Ming. "On the multiplicity of Laplacian eigenvalues of graphs." Czechoslovak Mathematical Journal 60.3 (2010): 689-698. <http://eudml.org/doc/38036>.

@article{Guo2010,
abstract = {In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered.},
author = {Guo, Ji-Ming, Feng, Lin, Zhang, Jiong-Ming},
journal = {Czechoslovak Mathematical Journal},
keywords = {Laplacian eigenvalue; multiplicity; tree; characteristic polynomial; Laplacian eigenvalue; multiplicity; tree; characteristic polynomial},
language = {eng},
number = {3},
pages = {689-698},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the multiplicity of Laplacian eigenvalues of graphs},
url = {http://eudml.org/doc/38036},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Guo, Ji-Ming
AU - Feng, Lin
AU - Zhang, Jiong-Ming
TI - On the multiplicity of Laplacian eigenvalues of graphs
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 689
EP - 698
AB - In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered.
LA - eng
KW - Laplacian eigenvalue; multiplicity; tree; characteristic polynomial; Laplacian eigenvalue; multiplicity; tree; characteristic polynomial
UR - http://eudml.org/doc/38036
ER -

References

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  1. Cvetković, D. M., Doob, M., Sachs, H., Spectra of Graphs-Theory and Application, Deutscher Verlag der Wissenschaften - Academic Press, Berlin-New York, 1980; second edition 1982; third edition, Johann Ambrosius Barth Verlag, Heidelberg-Leipzig (1995). (1995) 
  2. Faria, I., 10.1016/0024-3795(85)90281-2, Linear Algebra Appl. 64 (1985), 255-265. (1985) Zbl0559.05041MR0776531DOI10.1016/0024-3795(85)90281-2
  3. Grone, R., Merris, R., Sunder, V. S., 10.1137/0611016, SIAM J. Matrix Anal. Appl. 11 (1990), 218-238. (1990) Zbl0733.05060MR1041245DOI10.1137/0611016
  4. Grone, R., Merris, R., 10.1137/S0895480191222653, SIAM J. Discrete Math. 7 (1994), 221-229. (1994) Zbl0795.05092MR1271994DOI10.1137/S0895480191222653
  5. Guo, J. M., 10.1016/j.laa.2005.02.031, Linear Alg. Appl. 404 (2005), 251-261. (2005) Zbl1066.05085MR2149662DOI10.1016/j.laa.2005.02.031
  6. Mohar, B., The Laplacian spectrum of graphs, Graph Theory, Combinatorics, and Applications 2 (1991), 871-898. (1991) Zbl0840.05059MR1170831
  7. Shao, J. Y., Guo, J. M., Shan, H. Y., The ordering of trees and connected graphs by algebraic connectivity, Linear Alg. Appl. 428 (2008), 1421-1438. (2008) Zbl1134.05063MR2388629

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