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2006 | 26 | 1 | 49-58
Tytuł artykułu

Spectral integral variation of trees

Autorzy
Treść / Zawartość
Warianty tytułu
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.
Wydawca
Rocznik
Tom
26
Numer
1
Strony
49-58
Opis fizyczny
Daty
wydano
2006
otrzymano
2004-10-11
poprawiono
2005-01-08
Twórcy
autor
  • School of Mathematics and Computational Science, Anhui University, Hefei, Anhui 230039, P.R. China
autor
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1300
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