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Bounds for the Least Laplacian Eigenvalue of a Signed Graph 被引量：5

Bounds for the Least Laplacian Eigenvalue of a Signed Graph
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摘要 A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated. A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated.
作者 Yao Ping HOU
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第4期955-960,共6页 数学学报（英文版）
基金 supported by the NSF of China(No.19971056) SRP(No.03B019) from the Education Committee of Hunan Province
关键词 Signed graph Laplacian matrix The least eigenvalue Balanced signed graph Signed graph, Laplacian matrix, The least eigenvalue, Balanced signed graph
分类号 O175.3 [理学—基础数学]
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参考文献11

  • 1Fiedler, M.: Algebraic connectivity of graphs. Czechoslovak Math. J., 23(1), 298-305 (1973).
  • 2Merris, R.: Laplacian Matrices of Graphs: A Survey. Linear Algebra and its Applications, 197/198(1),143-176 (1994).
  • 3Mohar, B.: Some applications of Laplacian eigenvalues of graphs, Graph Symmetry (G. Hahn and G. Sabidussi, eds.), Kluwer Academic Publishers, Boston, 225-275, 1997.
  • 4Chung, F. R.: Spectral Graph Theory, CBMS Lecture Notes, AMS Publication, 1997.
  • 5Harary, F.: On the notion of balanced in a signed graph. Michigan Math. J., 2(1), 143-146 (1953).
  • 6Deradass, B., Archarya, L.: Spectral criterion for cycle balance in networks. J. of Graph Theory, 4(1), 1-11(1980).
  • 7Zaslavsky, T.: Signed graphs. Discrete Appl. Math., 4(1), 47-74 (1982).
  • 8Chaiken, S.: A combinatorial proof of the all minors matrix tree theorem. SIAM J. Algebraic Discrete Methods, 3(2), 319-329 (1982).
  • 9Cameron, P. J., Seidel, J., Tsaranov, J. J.: Signed graphs, root lattices, and Coxeter groups. J. of Algebra,164(1), 173-209 (1994).
  • 10Hou, Y. P., Li, J. S.: On the Laplacian eigenvalues of signed graphs. Linear and Mutilinear Algebra, 51(1),21-30 (2003).

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Acta Mathematica Sinica,English Series
2005年 第4期

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