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On Laplacian energy in terms of graph invariants

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  • Das, Kinkar Ch.
  • Mojallal, Seyed Ahmad
  • Gutman, Ivan

Abstract

For G being a graph with n vertices and m edges, and with Laplacian eigenvalues μ1≥μ2≥⋯≥μn−1≥μn=0, the Laplacian energy is defined as LE=∑i=1n|μi−2m/n|. Let σ be the largest positive integer such that μσ ≥ 2m/n. We characterize the graphs satisfying σ=n−1. Using this, we obtain lower bounds for LE in terms of n, m, and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, m, maximum degree, vertex cover number, and spanning tree packing number.

Suggested Citation

  • Das, Kinkar Ch. & Mojallal, Seyed Ahmad & Gutman, Ivan, 2015. "On Laplacian energy in terms of graph invariants," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 83-92.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:83-92
    DOI: 10.1016/j.amc.2015.06.064
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    References listed on IDEAS

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    1. Li, Xueliang & Qin, Zhongmei & Wei, Meiqin & Gutman, Ivan & Dehmer, Matthias, 2015. "Novel inequalities for generalized graph entropies – Graph energies and topological indices," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 470-479.
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    Cited by:

    1. Das, Kinkar Ch. & Mojallal, Seyed Ahmad & Gutman, Ivan, 2016. "On energy and Laplacian energy of bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 759-766.
    2. Gersema, Gerke & Wozabal, David, 2017. "An equilibrium pricing model for wind power futures," Energy Economics, Elsevier, vol. 65(C), pages 64-74.
    3. Das, Kinkar Ch. & Mojallal, Seyed Ahmad, 2016. "Extremal Laplacian energy of threshold graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 267-280.

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