IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v422y2015icp193-202.html
   My bibliography  Save this article

Asymptotic incidence energy of lattices

Author

Listed:
  • Liu, Jia-Bao
  • Pan, Xiang-Feng

Abstract

The energy of a graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. As an analogue to E(G), the incidence energy IE(G), defined as the sum of the singular values of the incidence matrix of G, is a much studied quantity with well known applications in chemical physics. In this paper, based on the results by Yan and Zhang (2009), we propose the incidence energy per vertex problem for lattice systems, and present the closed-form formulae expressing the incidence energy of the hexagonal lattice, triangular lattice, and 33.42 lattice, respectively. Moreover, we show that the incidence energy per vertex of lattices is independent of the toroidal, cylindrical, and free boundary conditions. In particular, the explicit asymptotic values of the incidence energy in these lattices are obtained by utilizing the applications of analysis approach with the help of calculational software.

Suggested Citation

  • Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "Asymptotic incidence energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 193-202.
    • Handle: RePEc:eee:phsmap:v:422:y:2015:i:c:p:193-202
    DOI: 10.1016/j.physa.2014.12.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114010413
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.12.006?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. Yan, Weigen & Zhang, Zuhe, 2009. "Asymptotic energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1463-1471.
    2. Liu, Xiaoyun & Yan, Weigen, 2013. "The triangular kagomé lattices revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5615-5621.
    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. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    2. Song, Jingjing & Wallin, Fredrik & Li, Hailong, 2017. "District heating cost fluctuation caused by price model shift," Applied Energy, Elsevier, vol. 194(C), pages 715-724.
    3. Leurent, Martin & Jasserand, Frédéric & Locatelli, Giorgio & Palm, Jenny & Rämä, Miika & Trianni, Andrea, 2017. "Driving forces and obstacles to nuclear cogeneration in Europe: Lessons learnt from Finland," Energy Policy, Elsevier, vol. 107(C), pages 138-150.
    4. Webber, Phil & Gouldson, Andy & Kerr, Niall, 2015. "The impacts of household retrofit and domestic energy efficiency schemes: A large scale, ex post evaluation," Energy Policy, Elsevier, vol. 84(C), pages 35-43.
    5. Jia-Bao Liu & Mobeen Munir & Amina Yousaf & Asim Naseem & Khudaija Ayub, 2019. "Distance and Adjacency Energies of Multi-Level Wheel Networks," Mathematics, MDPI, vol. 7(1), pages 1-9, January.
    6. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
    7. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "A unified approach to the asymptotic topological indices of various lattices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 62-73.
    8. Shin, Kong Joo & Managi, Shunsuke, 2017. "Liberalization of a retail electricity market: Consumer satisfaction and household switching behavior in Japan," Energy Policy, Elsevier, vol. 110(C), pages 675-685.

    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. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "A unified approach to the asymptotic topological indices of various lattices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 62-73.
    2. Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.
    3. Liu, Xiaoyun & Yan, Weigen, 2013. "The triangular kagomé lattices revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5615-5621.
    4. Li, Shuli & Yan, Weigen, 2016. "Dimers on the 33.42 lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 251-257.
    5. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.

    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:phsmap:v:422:y:2015:i:c:p:193-202. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.