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Discussiones Mathematicae Graph Theory 26(1) (2006) 49-58
DOI: https://doi.org/10.7151/dmgt.1300

SPECTRAL INTEGRAL VARIATION OF TREES

Yi Wang and Yi-Zheng Fan

School of Mathematics and Computational Science
Anhui University, Hefei, Anhui 230039, P.R. China
e-mail: fanyz@ahu.edu.cn

Abstract

In this paper, we determine all trees with the property that adding a particular edge will result in exactly two Laplacian eigenvalues increasing respectively by 1 and the other Laplacian eigenvalues remaining fixed. We also investigate a situation in which the algebraic connectivity is one of the changed eigenvalues.

Keywords: tree, Laplacian eigenvalues, spectral integral variation, algebraic connectivity.

2000 Mathematics Subject Classification: 05C50, 15A18.

References

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Received 11 October 2004
Revised 8 January 2005