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2010 | 30 | 1 | 85-93
Tytuł artykułu

The signless Laplacian spectral radius of graphs with given number of cut vertices

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.
Wydawca
Rocznik
Tom
30
Numer
1
Strony
85-93
Opis fizyczny
Daty
wydano
2010
otrzymano
2008-04-25
poprawiono
2009-01-02
zaakceptowano
2009-03-12
Twórcy
autor
  • School of Mathematical Sciences, Anhui University, Hefei 230039, P.R. China
autor
  • School of Mathematical Sciences, Anhui University, Hefei 230039, P.R. China
Bibliografia
  • [1] W.N. Anderson and T.D. Morely, Eigenvalues of the Laplacian of a graph, Linear Multilinear Algebra 18 (1985) 141-145, doi: 10.1080/03081088508817681.
  • [2] A. Berman and X.-D. Zhang, On the spectral radius of graphs with cut vertices, J. Combin. Theory (B) 83 (2001) 233-240, doi: 10.1006/jctb.2001.2052.
  • [3] D. Cvetković, M. Doob and H. Sachs, Spectra of graphs, (third ed., Johann Ambrosius Barth Verlag, Heidelberg-Leipzig, 1995).
  • [4] D. Cvetković, Signless Laplacians and line graphs, Bull. Acad. Serbe Sci. Ars. Cl. Sci. Math. Nat. Sci. Math. 131 (30) (2005) 85-92.
  • [5] D. Cvetković, P. Rowlinson and S.K. Simić, Signless Laplacians of finite graphs, Linear Algebra Appl. 423 (2007) 155-171, doi: 10.1016/j.laa.2007.01.009.
  • [6] E.R. van Dam and W. Haemers, Which graphs are determined by their spectrum? Linear Algebra Appl. 373 (2003) 241-272, doi: 10.1016/S0024-3795(03)00483-X.
  • [7] M. Desai and V. Rao, A characterization of the smallest eigenvalue of a graph, J. Graph Theory 18 (1994) 181-194, doi: 10.1002/jgt.3190180210.
  • [8] Y.-Z. Fan, B.-S. Tam and J. Zhou, Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order, Linear Multilinear Algebra 56 (2008) 381-397, doi: 10.1080/03081080701306589.
  • [9] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.
  • [10] R. Grone and R. Merris, The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl. 11 (1990) 218-238, doi: 10.1137/0611016.
  • [11] J.W. Grossman, D.M. Kulkarni and I. Schochetman, Algebraic graph theory without orientation, Linear Algebra Appl. 212/213 (1994) 289-307, doi: 10.1016/0024-3795(94)90407-3.
  • [12] W. Haemer and E. Spence, Enumeration of cospectral graphs, Europ. J. Combin. 25 (2004) 199-211, doi: 10.1016/S0195-6698(03)00100-8.
  • [13] Q. Li and K.-Q. Feng, On the largest eigenvalues of graphs, (in Chinese), Acta Math. Appl. Sin. 2 (1979) 167-175.
  • [14] R. Merris, Laplacian matrices of graphs: A survey, Linear Algebra Appl. 197/198 (1994) 143-176, doi: 10.1016/0024-3795(94)90486-3.
  • [15] B. Mohar, Some applications of Laplacian eigenvalues of graphs, in: Graph Symmetry (G. Hahn and G. Sabidussi Eds), (Kluwer Academic Publishers, Dordrecht, 1997), 225-275.
  • [16] B.-S. Tam, Y.-Z. Fan and J. Zhou, Unoriented Laplacian maximizing graphs are degree maximal, Linear Algebra Appl. 429 (2008) 735-758, doi: 10.1016/j.laa.2008.04.002.
  • [17] Shangwang Tan and Xingke Wang, On the largest eigenvalue of signless Laplacian matrix of a graph, Journal of Mathematical Reserch and Exposion 29 (2009) 381-390.
  • [18] X.-D. Zhang and R. Luo, The Laplacian eigenvalues of a mixed graph, Linear Algebra Appl. 362 (2003) 109-119, doi: 10.1016/S0024-3795(02)00509-8.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1478
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