IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v346y2019icp559-574.html
   My bibliography  Save this article

Counting Clar structures of (4, 6)-fullerenes

Author

Listed:
  • Shi, Lingjuan
  • Zhang, Heping

Abstract

A (4, 6)-fullerene graph G is a plane cubic graph whose faces are squares and hexagons. A resonant set of G is a set of pairwise disjoint faces of G such that the boundaries of such faces are M-alternating cycles for a perfect matching M of G. A resonant set of G is referred to as sextet pattern whenever it only includes hexagonal faces. It was shown that the cardinality of a maximum resonant set of G is equal to the maximum forcing number. In this article, we obtain an expression for the cardinality of a maximum sextet pattern (or Clar formula) of G, which is less than the cardinality of a maximum resonant set of G by one or two. Moreover we mainly characterize all the maximum sextet patterns of G. Via such characterizations we get a formula to count maximum sextet patterns of G only depending on the order of G and the number of fixed subgraphs J1 of G, where the count equals the coefficient of the term with largest degree in its sextet polynomial. Also the number of Clar structures of G is obtained.

Suggested Citation

  • Shi, Lingjuan & Zhang, Heping, 2019. "Counting Clar structures of (4, 6)-fullerenes," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 559-574.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:559-574
    DOI: 10.1016/j.amc.2018.10.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318308932
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.10.027?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. Zhai, Shaohui & Alrowaili, Dalal & Ye, Dong, 2018. "Clar structures vs Fries structures in hexagonal systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 384-394.
    2. Yang Gao & Heping Zhang, 2014. "Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, August.
    Full references (including those not matched with items on IDEAS)

    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.

      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:346:y:2019:i:c:p:559-574. 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.