Research ArticleOpen AccessGoogle Scholar indexed
The Bounds for Eigenvalues of Normalized Laplacian Matrices and Signless Laplacian Matrices
Department of Mathematics, Faculty of Science, Gazi University, Ankara, Turkey
Institue of Science, Ahi Evran University, K?r?ehir, Turkey
- 1 Department of Mathematics, Faculty of Science, Gazi University, Ankara, Turkey
- 2 Institue of Science, Ahi Evran University, K?r?ehir, Turkey
Advances in Linear Algebra & Matrix Theory·Volume 04 (2014)·Pages 201–204·Published 14 November 2014·DOI10.4236/alamt.2014.44017
Copy link · social · email
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.
KeywordsNormalized Laplacian MatrixSignless Laplacian MatrixBounds of Eigenvalue
- 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
- 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
- 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
- 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
- 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