Spectral integral variation of trees
Yi Wang ; Yi-Zheng Fan
Discussiones Mathematicae Graph Theory, Tome 26 (2006), p. 49-58 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:270715 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1300,
     author = {Yi Wang and Yi-Zheng Fan},
     title = {Spectral integral variation of trees},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {26},
     year = {2006},
     pages = {49-58},
     zbl = {1103.05055},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1300}
}

Yi Wang; Yi-Zheng Fan. Spectral integral variation of trees. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 49-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1300/

[000] [1] D.M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs-Theory and Applications (2nd Edn., VEB Deutscher Verlag d. Wiss., Berlin, 1982). | Zbl 0824.05046

[001] [2] Yi-Zheng Fan, On spectral integral variations of graph, Linear and Multilinear Algebra 50 (2002) 133-142, doi: 10.1080/03081080290019513. | Zbl 0995.05094

[002] [3] Yi-Zheng Fan, Spectral integral variations of degree maximal graphs, Linear and Multilinear Algebra 52 (2003) 147-154.

[003] [4] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.

[004] [5] M. Fiedler, A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory, Czechoslovak Math. J. 25 (1975) 619-633. | Zbl 0437.15004

[005] [6] R. Grone, R. Merris and V.S. Sunder, The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl. 11 (1990) 218-238, doi: 10.1137/0611016. | Zbl 0733.05060

[006] [7] R. Grone and R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discrete Math. 7 (1994) 229-237, doi: 10.1137/S0895480191222653. | Zbl 0795.05092

[007] [8] F. Harary and A.J. Schwenk, Which graphs have integral spectra? in: Graphs and Combinatorics, R.A. Bari and F. Harray eds. (Springer-Verlag, 1974), 45-51, doi: 10.1007/BFb0066434.

[008] [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. | Zbl 1051.05060

[009] [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. | Zbl 0802.05053

[010] [11] R. Merris, Degree maximal graphs are Laplacian integral, Linear Algebra Appl. 199 (1994) 381-389, doi: 10.1016/0024-3795(94)90361-1. | Zbl 0795.05091

[011] [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. | Zbl 0840.05059

[012] [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. | Zbl 0935.05065