The signless Laplacian spectral radius of graphs with given number of cut vertices

Lin Cui; Yi-Zheng Fan

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 1, page 85-93
  • ISSN: 2083-5892

Abstract

top
In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.

How to cite

top

Lin Cui, and Yi-Zheng Fan. "The signless Laplacian spectral radius of graphs with given number of cut vertices." Discussiones Mathematicae Graph Theory 30.1 (2010): 85-93. <http://eudml.org/doc/270860>.

@article{LinCui2010,
abstract = {In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.},
author = {Lin Cui, Yi-Zheng Fan},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph; cut vertex; signless Laplacian matrix; spectral radius},
language = {eng},
number = {1},
pages = {85-93},
title = {The signless Laplacian spectral radius of graphs with given number of cut vertices},
url = {http://eudml.org/doc/270860},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Lin Cui
AU - Yi-Zheng Fan
TI - The signless Laplacian spectral radius of graphs with given number of cut vertices
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 1
SP - 85
EP - 93
AB - In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.
LA - eng
KW - graph; cut vertex; signless Laplacian matrix; spectral radius
UR - http://eudml.org/doc/270860
ER -

References

top
  1. [1] W.N. Anderson and T.D. Morely, Eigenvalues of the Laplacian of a graph, Linear Multilinear Algebra 18 (1985) 141-145, doi: 10.1080/03081088508817681. 
  2. [2] A. Berman and X.-D. Zhang, On the spectral radius of graphs with cut vertices, J. Combin. Theory (B) 83 (2001) 233-240, doi: 10.1006/jctb.2001.2052. Zbl1023.05098
  3. [3] D. Cvetković, M. Doob and H. Sachs, Spectra of graphs, (third ed., Johann Ambrosius Barth Verlag, Heidelberg-Leipzig, 1995). 
  4. [4] D. Cvetković, Signless Laplacians and line graphs, Bull. Acad. Serbe Sci. Ars. Cl. Sci. Math. Nat. Sci. Math. 131 (30) (2005) 85-92. Zbl1119.05066
  5. [5] D. Cvetković, P. Rowlinson and S.K. Simić, Signless Laplacians of finite graphs, Linear Algebra Appl. 423 (2007) 155-171, doi: 10.1016/j.laa.2007.01.009. Zbl1113.05061
  6. [6] E.R. van Dam and W. Haemers, Which graphs are determined by their spectrum? Linear Algebra Appl. 373 (2003) 241-272, doi: 10.1016/S0024-3795(03)00483-X. Zbl1026.05079
  7. [7] M. Desai and V. Rao, A characterization of the smallest eigenvalue of a graph, J. Graph Theory 18 (1994) 181-194, doi: 10.1002/jgt.3190180210. Zbl0792.05096
  8. [8] Y.-Z. Fan, B.-S. Tam and J. Zhou, Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order, Linear Multilinear Algebra 56 (2008) 381-397, doi: 10.1080/03081080701306589. Zbl1146.05032
  9. [9] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305. 
  10. [10] R. Grone and R. Merris, The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl. 11 (1990) 218-238, doi: 10.1137/0611016. Zbl0733.05060
  11. [11] J.W. Grossman, D.M. Kulkarni and I. Schochetman, Algebraic graph theory without orientation, Linear Algebra Appl. 212/213 (1994) 289-307, doi: 10.1016/0024-3795(94)90407-3. Zbl0817.05047
  12. [12] W. Haemer and E. Spence, Enumeration of cospectral graphs, Europ. J. Combin. 25 (2004) 199-211, doi: 10.1016/S0195-6698(03)00100-8. Zbl1033.05070
  13. [13] Q. Li and K.-Q. Feng, On the largest eigenvalues of graphs, (in Chinese), Acta Math. Appl. Sin. 2 (1979) 167-175. 
  14. [14] R. Merris, Laplacian matrices of graphs: A survey, Linear Algebra Appl. 197/198 (1994) 143-176, doi: 10.1016/0024-3795(94)90486-3. Zbl0802.05053
  15. [15] B. Mohar, Some applications of Laplacian eigenvalues of graphs, in: Graph Symmetry (G. Hahn and G. Sabidussi Eds), (Kluwer Academic Publishers, Dordrecht, 1997), 225-275. Zbl0883.05096
  16. [16] B.-S. Tam, Y.-Z. Fan and J. Zhou, Unoriented Laplacian maximizing graphs are degree maximal, Linear Algebra Appl. 429 (2008) 735-758, doi: 10.1016/j.laa.2008.04.002. Zbl1149.05034
  17. [17] Shangwang Tan and Xingke Wang, On the largest eigenvalue of signless Laplacian matrix of a graph, Journal of Mathematical Reserch and Exposion 29 (2009) 381-390. Zbl1212.05164
  18. [18] X.-D. Zhang and R. Luo, The Laplacian eigenvalues of a mixed graph, Linear Algebra Appl. 362 (2003) 109-119, doi: 10.1016/S0024-3795(02)00509-8. Zbl1017.05078

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.