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Anti-forcing spectrum of any cata-condensed hexagonal system is continuous

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Abstract

The anti-forcing number of a perfect matching M of a graph G is the minimal number of edges not in M whose removal makes M a unique perfect matching of the resulting graph. The anti-forcing spectrum of G is the set of anti-forcing numbers over all perfect matchings of G: In this paper, we prove that the anti-forcing spectrum of any cata-condensed hexagonal system is continuous, that is, it is a finite set of consecutive integers.

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Acknowledgements

The authors would like to sincerely thank the anonymous referees for providing some helpful comments and suggestions in improving the manuscript. This work was supported by the National Natural Science Foundation of China (Grants Nos. 11371180, 11401279).

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Authors and Affiliations

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

    Kai Deng & Heping Zhang

  2. School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, 750027, China

    Kai Deng

Authors
  1. Kai Deng
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  2. Heping Zhang
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Correspondence to Heping Zhang.

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Deng, K., Zhang, H. Anti-forcing spectrum of any cata-condensed hexagonal system is continuous. Front. Math. China 12, 325–337 (2017). https://doi.org/10.1007/s11464-016-0605-0

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  • DOI: https://doi.org/10.1007/s11464-016-0605-0

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