The Laplacian spectral radii of trees with degree sequences

Discrete Mathematics

Volumn 308, Issue 15, 2008, Pages 3143-3150

  Zhang, Xiao Dong ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Degree sequence; Laplacian spectral radius; Majorization; Tree

Indexed keywords

LAPLACE EQUATION; NUMERICAL METHODS; SPECTRUM ANALYSIS;

DEGREE SEQUENCES; LAPLACIAN SPECTRAL RADII; MAJORIZATION;

TREES (MATHEMATICS);

EID: 43249097543     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2007.06.017     Document Type: Article

References (12)

1. Anderson W.N., and Morley T.D. Eigenvalues of the Laplacian of a graph. Linear and Multilinear Algebra 18 (1985) 141-145
2. Erdös P., and Gallai T. Graphs with prescribed degrees of vertices (Hungarian). Mat. Lapok 11 (1960) 264-274
3. Grone R., and Merris R. The Laplacian spectrum of a graph. II. SIAM J. Discrete Math. 7 2 (1994) 221-229
4. Grone R., Merris R., and Sunder V.S. The Laplacian spectrum of a graph. SIAM J. Matrix Anal. Appl. 11 (1990) 218-238
5. Guo J.M. On the Laplacian spectral radius of a tree. Linear Algebra Appl. 368 (2003) 379-385
6. Li J.S., and Zhang X.D. A new upper bound for eigenvalues matrix of a graph. Linear Algebra Appl. 265 (1997) 93-100
7. Merris R. Laplacian matrices of graphs: a survey. Linear Algebra Appl. 197-198 (1994) 143-176
8. Rojo O. Improved bounds for the largest eigenvalue of trees. Linear Algebra Appl. 404 (2005) 297-304
9. Shu J.L., Hong Y., and Wen R.K. A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph. Linear Algebra Appl. 347 (2002) 123-129
10. Stevanović D. Bounding the largest eigenvalue of trees interms of the largest vertex degree. Linear Algebra Appl. 360 (2003) 35-42
11. Zhang X.D. On the two conjectures of Graffiti. Linear Algebra Appl. 385 (2004) 369-379
12. Zhang X.D., and Li J.S. The Laplacian spectrum of mixed graphs. Linear Algebra Appl. 351 (2002) 11-20