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2007 | 27 | 2 | 373-384
Tytuł artykułu

On the second largest eigenvalue of a mixed graph

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a mixed graph. We discuss the relation between the second largest eigenvalue λ₂(G) and the second largest degree d₂(G), and present a sufficient condition for λ₂(G) ≥ d₂(G).
Słowa kluczowe
Wydawca
Rocznik
Tom
27
Numer
2
Strony
373-384
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-05-29
poprawiono
2006-09-12
zaakceptowano
2006-09-12
Twórcy
autor
  • School of Mathematics and Computation Sciences, Anhui University, Hefei 230039, P.R. China
autor
  • School of Mathematics and Computation Sciences, Anhui University, Hefei 230039, P.R. China
autor
  • School of Mathematics and Computation Sciences, Anhui University, Hefei 230039, P.R. 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] R.B. Bapat, J.W. Grossman and D.M. Kulkarni, Edge version of the matrix tree theorem for trees, Linear and Multilinear Algebra 47 (2000) 217-229, doi: 10.1080/03081080008818646.
  • [3] Y.-Z. Fan, Largest eigenvalue of a unicyclic mixed graph, Applied Mathematics A Journal of Chinese Universities (English Series) 19 (2004) 140-148.
  • [4] Y.-Z. Fan, On the least eigenvalue of a unicyclic mixed graph, Linear and Multilinear Algebra 53 (2005) 97-113, doi: 10.1080/03081080410001681540.
  • [5] Y.-Z. Fan, On spectral integral variations of mixed graphs, Linear Algebra Appl. 374 (2003) 307-316, doi: 10.1016/S0024-3795(03)00575-5.
  • [6] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.
  • [7] M. Fiedler, A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory, Czechoslovak Math. J. 25 (1975) 619-633.
  • [8] R. Grone and R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discrete Math. 7 (1994) 221-229, doi: 10.1137/S0895480191222653.
  • [9] J.-M. Guo and S.-W. Tan, A relation between the matching number and the Laplacian spectrum of a graph, Linear Algebra Appl. 325 (2001) 71-74, doi: 10.1016/S0024-3795(00)00333-5.
  • [10] R.A. Horn and C.R. Johnson, Matrix Analysis (Cambridge Univ. Press, Cambridge, 1985).
  • [11] 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.
  • [12] J.-S. Li and Y.-L. Pan, A note on the second largest eigenvalue of the Laplacian matrix of a graph, Linear and Multilinear Algebra 48 (2000) 117-121, doi: 10.1080/03081080008818663.
  • [13] R. Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl. 197/198 (1998) 143-176, doi: 10.1016/0024-3795(94)90486-3.
  • [14] 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.
  • [15] 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.
  • [16] X.-D. Zhang and R. Luo, The Laplacian eigenvalues of a mixed graph, Linear Algebra Appl. 353 (2003) 109-119, doi: 10.1016/S0024-3795(02)00509-8.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1368
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