Monomer–dimer model on a scale-free small-world network
Monomer–dimer model on a scale-free small-world network
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DOI：
10.1016/j.physa.2011.08.007
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发表时间：
2012-02
影响因子：
3.3
通讯作者：
Zhongzhi Zhang;Y. Sheng;Qiang Jiang
中科院分区：
文献类型：
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作者：
Zhongzhi Zhang;Y. Sheng;Qiang Jiang
网络上单体-二聚体排列的数目的明确确定是一个理论挑战，并且单体-二聚体问题的精确解仅适用于边界上具有单个单体的少数极限图，例如，矩形格子和四次格子;然而，尽管大量的真实的系统同时表现出无标度和小世界结构，但对无标度小世界网络上的单体-二聚体问题的分析研究（甚至数值结果）仍然缺失。本文研究了定义在无标度小世界网络上的单体-二聚体问题，得到了网络上所有可能的单体-二聚体排列数的精确公式，并在此基础上确定了网络中单体-二聚体排列数的渐近增长常数.结果表明，所得到的渐近增长常数远小于与所研究的网络具有相同平均度的二维格点和Sierpinski分形对应的渐近增长常数，这从另一个方面表明，无标度网络与不具有幂律行为的规则格点和分形相比，具有根本不同的结构.
The explicit determination of the number of monomer–dimer arrangements on a network is a theoretical challenge, and exact solutions to monomer–dimer problem are available only for few limiting graphs with a single monomer on the boundary, e.g., rectangular lattice and quartic lattice; however, analytical research (even numerical result) for monomer–dimer problem on scale-free small-world networks is still missing despite the fact that a vast variety of real systems display simultaneously scale-free and small-world structures. In this paper, we address the monomer–dimer problem defined on a scale-free small-world network and obtain the exact formula for the number of all possible monomer–dimer arrangements on the network, based on which we also determine the asymptotic growth constant of the number of monomer–dimer arrangements in the network. We show that the obtained asymptotic growth constant is much less than its counterparts corresponding to two-dimensional lattice and Sierpinski fractal having the same average degree as the studied network, which indicates from another aspect that scale-free networks have a fundamentally distinct architecture as opposed to regular lattices and fractals without power-law behavior.