Geodesic
Tight bounds on the algebraic connectivity of a balanced binary tree
The electronic journal of linear algebra, Tome 6 (1999-2000), pp. 62-71.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, quite tight lower and upper bounds are obtained on the algebraic connectivity, namely, the second-smallest eigenvalue of the Laplacian matrix, of an unweighted balanced binary tree with k levels and hence n = 2 k $\Gamma 1$ vertices. This is accomplished by considering the inverse of a matrix of order k $\Gamma 1$ readily obtained from the Laplacian matrix. It is shown that the algebraic connectivity is 1=(2 k $\Gamma $2k + 3) + $O(1=2 2k )$.
Classification : 5C50, 15A48
Keywords: binary trees, Laplacian matrix, algebraic connectivity AMS subject 
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Molitierno, Jason J.; Neumann, Michael; Shader, Bryan L. Tight bounds on the algebraic connectivity of a balanced binary tree. The electronic journal of linear algebra, Tome 6 (1999-2000), pp. 62-71. http://geodesic.mathdoc.fr/item/ELA_1999-2000__6__a5/