Tight Bounds on the Algebraic Connectivity of a Balanced Binary Tree

Authors

Jason J. Molitierno, Sacred Heart UniversityFollow
Michael Neumann, University of Connecticut - Storrs
Bryan L. Shader, University of Wyoming

Document Type

Peer-Reviewed Article

Publication Date

2000

Abstract

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) + 0(1/2^2k).

Comments

Previously published. Reprinted here with publisher permission. Electronic Journal Of Linear Algebra 6 (2000): 62-71.

At the time of publication Jason Molitierno was affiliated with the Department of Mathematics, University of Connecticut, Storrs, Connecticut.

DOI

10.13001/1081-3810.1040

Recommended Citation

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