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The Laplacian spread of graphs

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Abstract

The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the graph. In this paper, bounds are obtained for the Laplacian spread of graphs. By the Laplacian spread, several upper bounds of the Nordhaus-Gaddum type of Laplacian eigenvalues are improved. Some operations on Laplacian spread are presented. Connected c-cyclic graphs with n vertices and Laplacian spread n − 1 are discussed.

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Authors and Affiliations

  1. School of Computer Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, P. R. China

    Zhifu You

  2. South China Normal University, Guangzhou, 510631, P. R. China

    Zhifu You & Bolian Liu

Authors
  1. Zhifu You
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  2. Bolian Liu
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Corresponding author

Correspondence to Bolian Liu.

Additional information

This work was supported by the NNSF of China (No. 11071088).

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You, Z., Liu, B. The Laplacian spread of graphs. Czech Math J 62, 155–168 (2012). https://doi.org/10.1007/s10587-012-0003-z

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  • DOI: https://doi.org/10.1007/s10587-012-0003-z

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