Spectral integral variation of trees

• Autorzy: Yi Wang , Yi-Zheng Fan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

tree; Laplacian eigenvalues; spectral integral variation; algebraic connectivity

Kategorie tematyczne

• 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 1
• Strony: 49-58

Daty

wydano

2006

otrzymano

2004-10-11

poprawiono

2005-01-08

Twórcy

autor

Yi Wang

• School of Mathematics and Computational Science, Anhui University, Hefei, Anhui 230039, P.R. China

autor

Yi-Zheng Fan

• School of Mathematics and Computational Science, Anhui University, Hefei, Anhui 230039, P.R. China

Bibliografia

• [1] D.M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs-Theory and Applications (2nd Edn., VEB Deutscher Verlag d. Wiss., Berlin, 1982).
• [2] Yi-Zheng Fan, On spectral integral variations of graph, Linear and Multilinear Algebra 50 (2002) 133-142, doi: 10.1080/03081080290019513.
• [3] Yi-Zheng Fan, Spectral integral variations of degree maximal graphs, Linear and Multilinear Algebra 52 (2003) 147-154.
• [4] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.
• [5] M. Fiedler, A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory, Czechoslovak Math. J. 25 (1975) 619-633.
• [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.
• [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.
• [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.
• [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.
• [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.
• [11] R. Merris, Degree maximal graphs are Laplacian integral, Linear Algebra Appl. 199 (1994) 381-389, doi: 10.1016/0024-3795(94)90361-1.
• [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.
• [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.

Identyfikatory

DOI

10.7151/dmgt.1300