Document Type

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 = 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).

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.

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