The architecture and the Jones polynomial of polyhedral links

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	The architecture and the Jones polynomial of polyhedral links
	Jin, Xian'an ; Zhang, Fuji ; Zhang FJ(张福基)
刊名	http://dx.doi.org/10.1007/s10910-011-9876-6
	2011-10
关键词	DNA BRANCHED JUNCTIONS TUTTE POLYNOMIALS MOLECULAR DESIGN SIGNED GRAPHS KAUFFMAN BRACKETS CHAIN POLYNOMIALS KNOT-THEORY ZEROS FAMILIES OCTAHEDRON
英文摘要	National Natural Science Foundation of China [10831001]; Fundamental Research Funds for the Central Universities [2010121007]; In this paper, we first recall some known architectures of polyhedral links (Qiu and Zhai in J Mol Struct (THEOCHEM) 756:163-166, 2005; Yang and Qiu in MATCH Commun Math Comput Chem 58:635-646, 2007; Qiu et al. in Sci China Ser B Chem 51:13-18, 2008; Hu et al. in J Math Chem 46:592-603, 2009; Cheng et al. in MATCH Commun Math Comput Chem 62:115-130, 2009; Cheng et al. in MATCH Commun Math Comput Chem 63:115-130, 2010; Liu et al. in J Math Chem 48:439-456 2010). Motivated by these architectures we introduce the notions of polyhedral links based on edge covering, vertex covering, and mixed edge and vertex covering, which include all polyhedral links in Qiu and Zhai (J Mol Struct (THEOCHEM) 756:163-166, 2005), Yang and Qiu (MATCH Commun Math Comput Chem 58:635-646, 2007), Qiu et al. (Sci China Ser B Chem 51:13-18, 2008), Hu et al. (J Math Chem 46:592-603, 2009), Cheng et al. (MATCH Commun Math Comput Chem 62:115-130, 2009), Cheng et al. (MATCH Commun Math Comput Chem 63:115-130, 2010), Liu et al. (J Math Chem 48:439-456, 2010) as special cases. The analysis of chirality of polyhedral links is very important in stereochemistry and the Jones polynomial is powerful in differentiating the chirality (Flapan in When topology meets chemistry. Cambridge Univ. Press, Cambridge, 2000). Then we give a detailed account of a result on the computation of the Jones polynomial of polyhedral links based on edge covering developed by Jin, Zhang, Dong and Tay (Electron. J. Comb. 17(1): R94, 2010) and, at the same time, by using this method we obtain some new computational results on polyhedral links of rational type and uniform polyhedral links with small edge covering units. These new computational results are helpful to judge the chirality of polyhedral links based on edge covering. Finally, we give some remarks and pose some problems for further study.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66296]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Jin, Xian'an,Zhang, Fuji,Zhang FJ. The architecture and the Jones polynomial of polyhedral links[J]. http://dx.doi.org/10.1007/s10910-011-9876-6,2011.
APA	Jin, Xian'an,Zhang, Fuji,&张福基.(2011).The architecture and the Jones polynomial of polyhedral links.http://dx.doi.org/10.1007/s10910-011-9876-6.
MLA	Jin, Xian'an,et al."The architecture and the Jones polynomial of polyhedral links".http://dx.doi.org/10.1007/s10910-011-9876-6 (2011).