Extremal polyomino chains on k-matchings and k-independent sets

Denote by the set of polyomino chains with n squares. For any , let mk(Tn) and ik(Tn) be the number of k-matchings and k-independent sets of Tn, respectively. In this paper, we show that for any polyomino chain and any , and , with the left equalities holding for all k only if Tn=Ln, and the right e...

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Bibliographic Details
Published in:Journal of mathematical chemistry 2007-08, Vol.42 (2), p.125-140
Main Authors: Zeng, Yanqiu, Zhang, Fuji
Format: Article
Language:English
Subjects:
Chains
Chemistry
Exact sciences and technology
General and physical chemistry
Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
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Summary:Denote by the set of polyomino chains with n squares. For any , let mk(Tn) and ik(Tn) be the number of k-matchings and k-independent sets of Tn, respectively. In this paper, we show that for any polyomino chain and any , and , with the left equalities holding for all k only if Tn=Ln, and the right equalities holding for all k only if Tn=Zn, where Ln and Zn are the linear chain and the zig-zag chain, respectively.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-005-9039-8