IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v268y2015icp83-92.html
   My bibliography  Save this article

On Laplacian energy in terms of graph invariants

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315008450
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.06.064?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Li, Hong-Hai & Wu, Qian-Qian & Gutman, Ivan, 2016. "On ordering of complements of graphs with respect to matching numbers," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 167-174.
    3. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2015. "An inequality between the edge-Wiener index and the Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 714-721.
    4. Milovanović, Igor & Milovanović, Emina & Gutman, Ivan, 2016. "Upper bounds for some graph energies," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 435-443.
    5. Safaei, F. & Yeganloo, H. & Akbar, R., 2020. "Robustness on topology reconfiguration of complex networks: An entropic approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 379-409.
    6. Rodríguez, José M. & Sigarreta, José M., 2016. "Spectral properties of geometric–arithmetic index," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 142-153.
    7. Ghorbani, Modjtaba & Dehmer, Matthias & Zangi, Samaneh, 2018. "Graph operations based on using distance-based graph entropies," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 547-555.
    8. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.
    9. Das, Kinkar Ch. & Mojallal, Seyed Ahmad, 2016. "Extremal Laplacian energy of threshold graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 267-280.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:83-92. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.