On the monomer-dimer problem of some graphs

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	On the monomer-dimer problem of some graphs
	Yan, Weigen; Yeh, Yeong-Nan
	2008-05-01
发表期刊	STUDIES IN APPLIED MATHEMATICS
ISSN	0022-2526
卷号	120 期号:4 页码:351-360
摘要	The pure-dimer problem was solved in exact closed form for many lattice graphs. Although some numerical solutions of the monomer-dimer problem were obtained, no exact solutions of the monomer-dimer problem were available (except in one dimension). Let G be an arbitrary graph with N vertices. Construct a new graph R(G) from G by adding a new verex e* corresponding to each edge e = (a, b) of G and by joining each new vertex e* to the vertices a and b. If the suitable activities of vertices and edges in R(G) are selected, then the monomer-dimer problem can be solved exactly for the graph R(G), which generalizes the result obtained by Yan and Yeh. As applications, if we select suitable activities for the vertices and edges of R((L) over tilde (n,d)), we obtain the exact formulae for the MD partition function, MD free energy, and MD entropy of R((L) over tilde (n,d)) for the d-dimensional lattice (L) over tilde (n,d)) with periodic boundaries.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000255517600002
出版者	WILEY-BLACKWELL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6119
专题	中国科学院数学与系统科学研究院
通讯作者	Yan, Weigen
作者单位	Jimei Univ, Sch Sci, Inst Math, Acad Sinica, Xiamen 361021, Peoples R China
推荐引用方式 GB/T 7714	Yan, Weigen,Yeh, Yeong-Nan. On the monomer-dimer problem of some graphs[J]. STUDIES IN APPLIED MATHEMATICS,2008,120(4):351-360.
APA	Yan, Weigen,&Yeh, Yeong-Nan.(2008).On the monomer-dimer problem of some graphs.STUDIES IN APPLIED MATHEMATICS,120(4),351-360.
MLA	Yan, Weigen,et al."On the monomer-dimer problem of some graphs".STUDIES IN APPLIED MATHEMATICS 120.4(2008):351-360.