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2008 | 28 | 2 | 345-359
Tytuł artykułu

An upper bound on the Laplacian spectral radius of the signed graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.
Wydawca
Rocznik
Tom
28
Numer
2
Strony
345-359
Opis fizyczny
Daty
wydano
2008
otrzymano
2008-01-15
poprawiono
2008-04-21
zaakceptowano
2008-04-21
Twórcy
autor
  • College of Mathematic and Information Science, Jiangxi Normal University Nanchang, JiangXi, 330022 People's Republic of China
  • Department of Mathematics, University of Science and Technology of China, Anhui, Hefei 230026 People's Republic of China
Bibliografia
  • [1] R.B. Bapat, J.W. Grossman and D.M. Kulkarni, Generalized matrix tree theorem for mixed graphs, Linear and Multilinear Algebra 46 (1999) 299-312, doi: 10.1080/03081089908818623.
  • [2] F. Chung, Spectral Graph Theory (CMBS Lecture Notes. AMS Publication, 1997).
  • [3] D.M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs (Academic Press, New York, 1980).
  • [4] J.M. Guo, A new upper bound for the Laplacian spectral radius of graphs, Linear Algebra Appl. 400 (2005) 61-66, doi: 10.1016/j.laa.2004.10.022.
  • [5] F. Harary, On the notion of balanced in a signed graph, Michigan Math. J. 2 (1953) 143-146, doi: 10.1307/mmj/1028989917.
  • [6] R.A. Horn and C.R. Johnson, Matrix Analysis (Cambridge Univ. Press, 1985).
  • [7] Y.P. Hou, J.S. Li and Y.L. Pan, On the Laplacian eigenvalues of signed graphs, Linear and Multilinear Algebra 51 (2003) 21-30, doi: 10.1080/0308108031000053611.
  • [8] L.L. Li, A simplified Brauer's theorem on matrix eigenvalues, Appl. Math. J. Chinese Univ. (B) 14 (1999) 259-264, doi: 10.1007/s11766-999-0034-x.
  • [9] R. Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl. 197 (1994) 143-176, doi: 10.1016/0024-3795(94)90486-3.
  • [10] T.F. Wang, Several sharp upper bounds for the largest Laplacian eigenvalues of a graph, to appear.
  • [11] T. Zaslavsky, Signed graphs, Discrete Appl. Math. 4 (1982) 47-74, doi: 10.1016/0166-218X(82)90033-6.
  • [12] X.D. Zhang, Two sharp upper bounds for the Laplacian eigenvalues, Linear Algebra Appl. 376 (2004) 207-213, doi: 10.1016/S0024-3795(03)00644-X.
  • [13] X.D. Zhang and J.S. Li, The Laplacian spectrum of a mixed graph, Linear Algebra Appl. 353 (2002) 11-20, doi: 10.1016/S0024-3795(01)00538-9.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1410
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