ALAMT  Vol.4 No.4 , December 2014
The Bounds for Eigenvalues of Normalized Laplacian Matrices and Signless Laplacian Matrices
ABSTRACT
In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.

Cite this paper
Büyükköse, S. and Eski, S. (2014) The Bounds for Eigenvalues of Normalized Laplacian Matrices and Signless Laplacian Matrices. Advances in Linear Algebra & Matrix Theory, 4, 201-204. doi: 10.4236/alamt.2014.44017.
References
[1]   Oliveira, C.S., De Lima, L.S., De Abreu, N.M.M. and Hansen, P. (2010) Bound on the Index of the Signless Laplacian of a Graph. Discrete Applied Mathematics, 158, 355-360.
http://dx.doi.org/10.1016/j.dam.2009.06.023

[2]   Li, J. and Pan, Y. (2004) Upper Bounds for the Laplacian Graph Eigenvalues. Acta Mathematica Sinica, English Series, 20, 803-806.
http://dx.doi.org/10.1007/s10114-004-0332-4

[3]   Liu, H., Lu, M. and Tian, F. (2004) On the Laplacian Spectral Radius of a Graph. Linear Algebra and Its Applications, 376, 135-141.
http://dx.doi.org/10.1016/j.laa.2003.06.007

[4]   Rojo, O. and Soto, R.L. (2013) A New Upper Bound on the Largest Normalized Laplacian Eigenvals. Operators and Matrices, 7, 323-332.
http://dx.doi.org/10.7153/oam-07-19

[5]   Wolkowich, H. and Styan, G.P.H. (1980) Bounds for Eigenvalues Using Traces of Matrice. Linear Algebra and Its Applications, 29, 471-506.
http://dx.doi.org/10.1016/0024-3795(80)90258-X

 
 
Top