Bounds on the (Laplacian) spectral radius of graphs

Linear Algebra and Its Applications

Volumn 422, Issue 2-3, 2007, Pages 755-770

  Shi, Lingsheng ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Laplacian spectral radius; Nordhaus Gaddum type; Spectral radius

Indexed keywords

COMPUTATIONAL COMPLEXITY; EIGENVALUES AND EIGENFUNCTIONS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA;

ADJACENCY MATRIX; CONNECTED GRAPHS; DIAGONAL MATRIX; NORDHAUS-GADDUM TYPE; SPECTRAL RADIUS;

GRAPH THEORY;

EID: 33847301110     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2006.12.003     Document Type: Article

References (23)

1. Alari C.Y., Chartrand G., Ollermann O.R., and Schwenk A.J. Graph Theory, Combinatorics and Applications (1991), Wiley, New York pp. 871-898
2. Cao D. Bounds on eigenvalues and chromatic numbers. Linear Algebra Appl. 270 (1998) 1-13
3. Cvetković D., Doob M., and Sachs H. Spectra of Graphs - Theory and Application (1980), Academic Press, New York
4. Das K.Ch., and Kumar P. Some new bounds on the spectral radius of graphs. Discrete Math. 281 (2004) 149-161
5. Ellingham M.N., and Zha X. The spectral radius of graphs on surface. J. Combin. Thoery Ser. B 78 (2000) 45-56
6. Favaron O., Mahéo M., and Saclé J.-F. Some eigenvalue properties in graphs (conjectures of Graffiti. II). Discrete Math. 111 (1993) 197-200
7. Fiedler M. Algebraic connectivity of graphs. Czechoslovak Math. J. 23 (1973) 298-305
8. Hong Y., Shu J., and Fang K. A sharp upper bound of the spectral radius of graphs. J. Combin. Theory Ser. B 81 (2001) 177-183
9. Hong Y., and Zhang X. Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees. Discrete Math. 296 (2005) 187-197
10. Li J., and Pan Y. de Cane's inequality and bounds on the largest Laplacian eigenvalue of a graph. Linear Algebra Appl. 328 (2001) 153-160
11. Li X. The relations between the spectral radius of the graphs and their complement. J. North China Technol. Inst. 17 4 (1996) 297-299
12. B. Liu, J. Shen, On the largest eigenvalue of nonregular graphs, preprint.
13. Liu H., Lu M., and Tian F. On the Laplacian spectral radius of a graph. Linear Algebra Appl. 376 (2004) 135-141
14. Lu M., Liu H., and Tian F. Bounds of Laplacian spectrum of graphs based on the domination number. Linear Algebra Appl. 402 (2004) 390-396
15. Nikiforov V. Walks and the spectral radius of graphs. Linear Algebra Appl. 418 (2006) 257-268
16. Nordhaus E.A., and Gaddum J.M. On complementary graphs. Amer. Math. Monthly 63 (1956) 175-177
17. E. Nosal, Eigenvalues of graphs, Master Thesis, University of Calgary, 1970.
18. Petrović M., and Gutman I. The path is the tree with smallest greatest Laplacian eigenvalue. Kragujevac J. Math. 24 (2002) 67-70
19. Stevanović D. The largest eigenvalue of nonregular graphs. J. Combin. Theory Ser. B 91 (2004) 143-146
20. Yu A., Lu M., and Tian F. On the spectral radius of graphs. Linear Algebra Appl. 387 (2004) 41-49
21. Yuan X. The spectral radius of Laplace matrix of graphs, Master Thesis (2003), East China Normal University, China
22. Zhang X. Eigenvectors and eigenvalues of nonregular graphs. Linear Algebra Appl. 409 (2005) 79-86
23. Zhang X., and Luo R. The spectral radius of triangle-free graphs. Australas. J. Combin. 26 (2002) 33-39