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 = 2k - 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/(2k - 2k + 3) + 0(1/22k).
Molitierno, J.J., Neumann, M. & Shader, B.L. (2000). Tight bounds on the algebraic connectivity of a balanced binary tree. Electronic Journal of Linear Algebra, 6(1), 62-71. doi: 10.13001/1081-3810.1040