ELA, Volume 6, pp. 62-71, March 2000, abstract.

Tight Bounds on the Algebraic Connectivity 
of a Balanced Binary Tree

Jason J. Molitierno, Michael Neumann, and Bryan L. Shader

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-1 vertices. This is 
accomplished  by considering the inverse of a  matrix  of order 
k-1 readily obtained from the Laplacian matrix. It is shown that
the algebraic connectivity is  1/(2^k-2k+3)+ O(1/2^{2k}).