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Monomer–dimer problem on some networks

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  • Wu, Ruijuan
  • Yan, Weigen

Abstract

Zhang et al. (2012) obtained the exact formula for the number of all possible monomer–dimer arrangements and the asymptotic growth constant on a scale-free small-world network. In this note, we generalize this result and obtain the exact solution on the monomer–dimer model on many networks. Particularly, we prove that these networks have the same asymptotic growth constant of the number of monomer–dimer arrangements.

Suggested Citation

  • Wu, Ruijuan & Yan, Weigen, 2016. "Monomer–dimer problem on some networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 465-468.
    • Handle: RePEc:eee:phsmap:v:457:y:2016:i:c:p:465-468
    DOI: 10.1016/j.physa.2016.03.065
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    References listed on IDEAS

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    1. Zhang, Zhongzhi & Sheng, Yibin & Jiang, Qiang, 2012. "Monomer–dimer model on a scale-free small-world network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 828-833.
    2. Chang, Shu-Chiuan & Chen, Lung-Chi, 2008. "Dimer-monomer model on the Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1551-1566.
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      Keywords

      Monomer–dimer model; Enumeration problem;

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