The spectrum of the laplacian matrix of a balanced 2?-ary tree
DOI:
https://doi.org/10.4067/S0716-09172004000200006Keywords:
Tree, balanced tree, binary tree, n−ary tree, Laplacian matrix, árbol, árbol balanceado, árbol binario, árbol n-ario, matriz Laplaciana.Abstract
References
[1] L. N. Trefethen and D. Bau, III, Numerical Linear Algebra, Society for Industrial and Applied Mathematics, (1997).
[2] A. Cantoni and P. Butler, Eigenvalues and eigenvectors of symmetric centrosymmetric matrices, Linear Algebra Appl. 13, pp. 275-288, (1976).
[3] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J., 23: pp. 298-305, (1973).
[4] G. H. Golub and C. F. Van Loan, Matrix Computations, 2d. ed., Baltimore: Johns Hopkins University Press, (1989).
[5] R. Grone, R Merris and V. S. Sunder, The Laplacian spectrum of a graph, SIAM J. Matrix Ana. Appl. 11 (2), pp. 218-238, (1990).
[6] F. B. Hildebrand, Finite-Difference Equations and Simulations, Prentice-Hall,Inc., Englewood Cliffs, N.J., (1968).
[7] R. Merris, Laplacian Matrices of Graphs: A Survey, Linear Algebra Appl. 197, 198: pp. 143-176, (1994).
[8] J. J. Molitierno, M. Neumann and B. L. Shader, Tight bounds on the algebraic connectivity of a balanced binary tree, Electronic Journal of Linear Algebra, Vol. 6, pp. 62-71, March (2000).
[9] O. Rojo, The spectrum of the Laplacian matrix of a balanced binary tree, Linear Algebra Appl. 349, pp. 203-219, (2002).
[10] O. Rojo and M. Peña, A note on the integer eigenvalues of the Laplacian matrix of a balanced binary tree, Linear Algebra Appl. 362, pp. 293-300 (2003).
[2] A. Cantoni and P. Butler, Eigenvalues and eigenvectors of symmetric centrosymmetric matrices, Linear Algebra Appl. 13, pp. 275-288, (1976).
[3] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J., 23: pp. 298-305, (1973).
[4] G. H. Golub and C. F. Van Loan, Matrix Computations, 2d. ed., Baltimore: Johns Hopkins University Press, (1989).
[5] R. Grone, R Merris and V. S. Sunder, The Laplacian spectrum of a graph, SIAM J. Matrix Ana. Appl. 11 (2), pp. 218-238, (1990).
[6] F. B. Hildebrand, Finite-Difference Equations and Simulations, Prentice-Hall,Inc., Englewood Cliffs, N.J., (1968).
[7] R. Merris, Laplacian Matrices of Graphs: A Survey, Linear Algebra Appl. 197, 198: pp. 143-176, (1994).
[8] J. J. Molitierno, M. Neumann and B. L. Shader, Tight bounds on the algebraic connectivity of a balanced binary tree, Electronic Journal of Linear Algebra, Vol. 6, pp. 62-71, March (2000).
[9] O. Rojo, The spectrum of the Laplacian matrix of a balanced binary tree, Linear Algebra Appl. 349, pp. 203-219, (2002).
[10] O. Rojo and M. Peña, A note on the integer eigenvalues of the Laplacian matrix of a balanced binary tree, Linear Algebra Appl. 362, pp. 293-300 (2003).
Published
2017-05-22
How to Cite
[1]
O. Rojo, “The spectrum of the laplacian matrix of a balanced 2?-ary tree”, Proyecciones (Antofagasta, On line), vol. 23, no. 2, pp. 131-149, May 2017.
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