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Bounding the sum of powers of the Laplacian eigenvalues of graphs

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Abstract

For a non-zero real number α, let s α (G) denote the sum of the αth power of the non-zero Laplacian eigenvalues of a graph G. In this paper, we establish a connection between s α (G) and the first Zagreb index in which the Hölder’s inequality plays a key role. By using this result, we present a lot of bounds of s α (G) for a connected (molecular) graph G in terms of its number of vertices (atoms) and edges (bonds). We also present other two bounds for s α (G) in terms of connectivity and chromatic number respectively, which generalize those results of Zhou and Trinajstić for the Kirchhoff index [B Zhou, N Trinajstić. A note on Kirchhoff index, Chem. Phys. Lett., 2008, 455: 120–123].

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, P.R. China

    Xiao-dan Chen & Jian-guo Qian

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  1. Xiao-dan Chen
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  2. Jian-guo Qian
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Correspondence to Jian-guo Qian.

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Supported by the National Natural Science Foundation of China (10831001).

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Chen, Xd., Qian, Jg. Bounding the sum of powers of the Laplacian eigenvalues of graphs. Appl. Math. J. Chin. Univ. 26, 142–150 (2011). https://doi.org/10.1007/s11766-011-2732-4

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  • DOI: https://doi.org/10.1007/s11766-011-2732-4

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