The third smallest eigenvalue of the Laplacian matrix

Electronic Journal of Linear Algebra

Volumn 8, Issue , 2001, Pages 128-139

  Patió, Sukanta ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

Author keywords

Algebraic connectivity; Laplacian matrix; Third smallest eigenvalue; Tree

Indexed keywords

EID: 3042662914     PISSN: 10813810     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. R. B. Bapat and S. Pati. Algebraic connectivity and the characteristic set of a graph. Linear and Multilinear Algebra, 45:247-273, 1998.
2. S. Fallat and S. Kirkland. Extremizing algebraic connectivity subject to graph theoretic constraints. Electronic Journal of Linear Algebra, 3:48-74, 1998.
3. S. Fallat, S. Kirkland, and S. Pati. Minimizing algebraic connectivity over connected graphs with fixed girth. Discrete Mathematics, to appear.
4. M. Fiedler. Algebraic connectivity of graphs. Czechoslovak Mathematical Journal, 23:298-305, 1973.
5. M. Fiedler. Eigenvectors of acyclic matrices. Czechoslovak Mathematical Journal, 25:607-618, 1975.
6. M. Fiedler. A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory. Czechoslovak Mathematical Journal, 25:619-633, 1975.
7. M. Fiedler. Laplacian of graphs and algebraic connectivity. Combinatorics and graph theory, Banach Centre Publications, Warsaw, 25:57-70, 1989.
8. R. Grone and R. Merris. Algebraic connectivity of trees. Czechoslovak Mathematical Journal, 37:660-670, 1987.
9. R. Grone, R. Merris, and V. S. Sunder. The Laplacian spectrum of a graph. SIAM Journal on Matrix Analysis and Applications, 11:218-238, 1990.
10. S. Kirkland and S. Fallat. Perron components and algebraic connectivity for weighted graphs. Linear and Multilinear Algebra, 44:131-148, 1998.
11. S. Kirkland, M. Neumann, and B. L. Shader. Characteristic vertices of weighted trees via Perron values. Linear and Multilinear Algebra, 40:311-325 1996.
12. S. Kirkland, M. Neumann, and B. L. Shader. Distances in weighted trees and group inverses of Laplacian matrices. SIAM Journal on Matrix Analysis and Applications, 18:827-841, 1997.
13. R. Merris. Characteristic vertices of trees. Linear and Multilinear Algebra, 22:115-131, 1987.
14. R.Merris. Laplacian matrices of graphs: a survey. Linear Algebra and its Applications, 197:143-176, 1994.
15. R. Merris. A survey of graph Laplacians. Linear and Multilinear Algebra, 39:19-31, 1995.
16. B. Mohar. Laplace eigenvalues of graphs-a survey. Discrete Mathematics, 109:171-183, 1992.
17. Y. L. Pan, J. S. Li, and Y. P. Hou. Lower bounds on the smallest Laplacian eigenvalue of a graph. Linear and Multilinear Algebra, to appear.