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Extremal hexagonal chains concerning k-matchings and k-independent sets

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Abstract

Denote by ℬ n the set of the hexagonal chains with n hexagons. For any B n ∈ℬ n , let m k (B n ) and i k (B n ) be the numbers of k-matchings and k-independent sets of B n , respectively. In the paper, we show that for any hexagonal chain B n ∈ℬ n and for any k≥0, m k (L n )≤m k (B n )≤m k (Z n ) and i k (L n )≥i k (B n )≥i k (Z n ), with left equalities holding for all k only if B n =L n , and the right equalities holding for all k only if B n =Z n , where L n and Z n are the linear chain and the zig-zag chain, respectively. These generalize some related results known before.

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Authors and Affiliations

  1. Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian, 363000, China

    Lian-zhu Zhang

  2. Department of Mathematics, Xiamen University, Xiamen, Fujian, 361005, China

    Fu-ji Zhang

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  1. Lian-zhu Zhang
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  2. Fu-ji Zhang
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Zhang, Lz., Zhang, Fj. Extremal hexagonal chains concerning k-matchings and k-independent sets. Journal of Mathematical Chemistry 27, 319–329 (2000). https://doi.org/10.1023/A:1018875823127

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