IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v425y2022ics0096300322001746.html
   My bibliography  Save this article

The anti-forcing spectra of (4,6)-fullerenes

Author

Listed:
  • Shi, Lingjuan
  • Zhang, Heping
  • Zhao, Lifang

Abstract

For an edge subset S of connected graph G, if G−S has only one perfect matching M, then S is called an anti-forcing set of M. The number of edges in a smallest anti-forcing set of M is the anti-forcing number of M, generally indicated by the symbol af(G,M). For a graph G, its anti-forcing spectrum is defined as the integer set Specaf(G):={af(G,M):M is a perfect matching of G}. In this paper, we show that for a (4,6)-fullerene graph Tn with cyclic edge-connectivity 3, Specaf(Tn)=[n+3,2n+4]. Moreover, we show that for any perfect matching M of a (4,6)-fullerene graph G, a minimum anti-forcing set S of M and each M-alternating facial boundary share exactly one edge. Applying this conclusion, we prove that the minimum anti-forcing number of a lantern structure (4,6)-fullerene of order n is ⌊n8⌋+2, and Specaf(Bn)=[⌊n8⌋+2,⌊n3⌋+2].

Suggested Citation

  • Shi, Lingjuan & Zhang, Heping & Zhao, Lifang, 2022. "The anti-forcing spectra of (4,6)-fullerenes," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001746
    DOI: 10.1016/j.amc.2022.127090
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322001746
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127090?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. Kai Deng & Heping Zhang, 2017. "Anti-forcing spectra of perfect matchings of graphs," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 660-680, February.
    2. Zhao, Shuang & Zhang, Heping, 2016. "Forcing polynomials of benzenoid parallelogram and its related benzenoids," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 209-218.
    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.
    1. Yaxian Zhang & Bo Zhang & Heping Zhang, 2022. "Anti-Forcing Spectra of Convex Hexagonal Systems," Mathematics, MDPI, vol. 10(19), pages 1-21, September.
    2. 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.
    3. Zhang, Yaxian & Zhang, Heping, 2022. "Continuous forcing spectrum of regular hexagonal polyhexes," Applied Mathematics and Computation, Elsevier, vol. 425(C).

    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:425:y:2022:i:c:s0096300322001746. 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.