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Continuous Forcing Spectra of Even Polygonal Chains

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Abstract

Let G be a graph that admits a perfect matching M. A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G. The cardinality of a forcing set of M with the smallest size is called the forcing number of M, denoted by f(G, M). The forcing spectrum of G is defined as: Spec(G) = {f(G, M)∣ M is a perfect matching of G}. In this paper, by applying the Z-transformation graph (resonance graph) we show that for any polyomino with perfect matchings and any even polygonal chain, their forcing spectra are integral intervals. Further we obtain some sharp bounds on maximum and minimum forcing numbers of hexagonal chains with given number of kinks. Forcing spectra of two extremal chains are determined.

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Acknowledgments

The authors are grateful to the referees for their careful reading and many valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, China

    He-ping Zhang

  2. School of Mathematics and Statistics, Huizhou University, Huizhou, 516007, China

    Xiao-yan Jiang

Authors
  1. He-ping Zhang
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  2. Xiao-yan Jiang
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Corresponding author

Correspondence to He-ping Zhang.

Additional information

This work is supported by the National Natural Science Foundation of China (Nos. 11871256, 11371180, 11226286).

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Zhang, Hp., Jiang, Xy. Continuous Forcing Spectra of Even Polygonal Chains. Acta Math. Appl. Sin. Engl. Ser. 37, 337–347 (2021). https://doi.org/10.1007/s10255-021-1010-3

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  • DOI: https://doi.org/10.1007/s10255-021-1010-3

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