Monomer-dimer model on a scale-free small-world network |
| |
Authors: | Zhongzhi Zhang Yibin ShengQiang Jiang |
| |
Affiliation: | a School of Computer Science, Fudan University, Shanghai 200433, Chinab Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433, Chinac School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
| |
Abstract: | 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. |
| |
Keywords: | Monomer-dimer model Scale-free network Enumeration problem |
本文献已被 ScienceDirect 等数据库收录! |
|