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

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  • 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
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    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.
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