Spectral integral variation of trees

Yi Wang; Yi-Zheng Fan

Discussiones Mathematicae Graph Theory (2006)

  • Volume: 26, Issue: 1, page 49-58
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Yi Wang, and Yi-Zheng Fan. "Spectral integral variation of trees." Discussiones Mathematicae Graph Theory 26.1 (2006): 49-58. <http://eudml.org/doc/270715>.

@article{YiWang2006,
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.},
author = {Yi Wang, Yi-Zheng Fan},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {tree; Laplacian eigenvalues; spectral integral variation; algebraic connectivity},
language = {eng},
number = {1},
pages = {49-58},
title = {Spectral integral variation of trees},
url = {http://eudml.org/doc/270715},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Yi Wang
AU - Yi-Zheng Fan
TI - Spectral integral variation of trees
JO - Discussiones Mathematicae Graph Theory
PY - 2006
VL - 26
IS - 1
SP - 49
EP - 58
AB - 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.
LA - eng
KW - tree; Laplacian eigenvalues; spectral integral variation; algebraic connectivity
UR - http://eudml.org/doc/270715
ER -

References

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  9. [9] S. Kirkland, A characterization of spectrum integral variation in two places for Laplacian matrices, Linear and Multilinear Algebra 52 (2004) 79-98, doi: 10.1080/0308108031000122506. Zbl1051.05060
  10. [10] R. Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl. 197/198 (1994) 143-176, doi: 10.1016/0024-3795(94)90486-3. Zbl0802.05053
  11. [11] R. Merris, Degree maximal graphs are Laplacian integral, Linear Algebra Appl. 199 (1994) 381-389, doi: 10.1016/0024-3795(94)90361-1. Zbl0795.05091
  12. [12] B. Mohar, The Laplacian spectrum of graphs, in: Y. Alavi et al. (eds.), Graph Theory, Combinatorics, and Applications (Wiley, New York, 1991) 871-898. Zbl0840.05059
  13. [13] W. So, Rank one perturbation and its application to the Laplacian spectrum of graphs, Linear and Multilinear Algebra 46 (1999) 193-198, doi: 10.1080/03081089908818613. Zbl0935.05065

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