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Sharp Upper and Lower Bounds for the Laplacian Spectral Radius and the Spectral Radius of Graphs

Sharp Upper and Lower Bounds for the Laplacian Spectral Radius and the Spectral Radius of Graphs
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摘要 In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, we also present sharp lower bounds for the Laplacian spectral radius and the spectral radius, respectively. In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, we also present sharp lower bounds for the Laplacian spectral radius and the spectral radius, respectively.
作者 Ji-ming Guo
机构地区 Department of Applied Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2008年第2期289-296,共8页 应用数学学报（英文版）
关键词 Graph Laplacian spectral radius spectral radius upper （lower） bound bipartite graph eigen-vector Graph, Laplacian spectral radius, spectral radius, upper （lower） bound, bipartite graph, eigen-vector
分类号 O157.6 [理学—基础数学]
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参考文献15

  • 1Anderson, W.N., Morley, T.D. Eigenvalues of the Laplacian of a graph. Linear and Multilinear Algebra, 18:141-145 (1985).
  • 2Berman, A., Zhang, X.D. On the spectral radius of graphs with cut vertices. J. Combin. Theory (Series B), 83:233-240 (2001).
  • 3Cvetkovic, D.M., Doob, M., Sachs, H. Spectra of graphs-Theory and Application. Deutscher Verlag der Wissenschaften - Academic Press, Berlin, New York, 1980; second edition 1982; third edition, Johann Ambrosius Barth Verlag, Heidelberg-Leipzig, 1995.
  • 4Das, K.C. A characterization on graphs which achieve the upper bound for the largest Laplacian eigenvalue of graphs. Linear Algebra Appl., 376:173-186 (2004).
  • 5Das, K.C., Kumar, P. Some new bounds on the spectral radius of graphs. Discrete Mathematics, 281:149-161 (2004).
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  • 7Guo, J.M. A new upper bound for the Laplacian spectral radius of graphs. Linear Algebra Appl., 400: 61-66 (2005).
  • 8Hong, Y. A hound on the spectral radius of graphs. Linear Algebra Appl., 108:135-140 (1988).
  • 9Hong, Y., Zhang, X.D. Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees. Discrete Mathematics, 296:187-197 (2005).
  • 10Horn, R.A., Johnson, C.R. Matrix Analysis. Cambridge University Press, New York, 1985.
Acta Mathematicae Applicatae Sinica
2008年 第2期

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