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	The replacements of signed graphs and Kauffman brackets of link families
	Jin, Xian&apos ; Zhang, Fuji ; an
	2007
关键词	Kauffman bracket graph polynomial signed graph rational link POLYNOMIALS KNOTS
英文摘要	Let G be a signed graph. Let 6 be the graph obtained from G by replacing each edge e of G by a chain or a sheaf. In this paper we first establish a relation between the Q-polynomial of (G) over cap [L.H. Kauffman, A Tutte polynomial for signed graphs, Discrete Appl. Math. 25 (1989) 105-127] and the W-polynomial of G [L. Traldi, A dichromatic polynomial for weighted graphs and link diagrams, Proc. Amer. Math. Soc. 106 (1989) 279-286; B. Bollobas, O. Riordan, A Tutte polynomial for colored graphs, Combin. Probab. Comput. 8 (1999) 45-93]. Then we derive two special dual cases from the relation, one of which has been obtained in [X. Jin, F. Zhang, The Kauffman brackets for equivalence classes of links, Adv. in Appl. Math. 34 (2005) 47-64]. Based on the one-to-one correspondence between signed plane graphs and link diagrams, and the correspondence between the Q-polynomial of a signed plane graph and the Kauffman bracket of a link diagram, we can compute the Kauffman bracket of the link diagram corresponding to 6 by means of the W-polynomial of G. In this way we investigate the Kauffman brackets of rational links as a typical link family, and obtain an explicit formula using transfer matrix approach. Finally we provide another link family to point out that the relation we built actually can be used to deal with Kauffman brackets of all such link families. (c) 2007 Elsevier Inc. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000247883500002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Applied; SCI(E); EI; 11; ARTICLE; 2; 155-172; 39
语种	英语
出处	SCI ; EI
出版者	应用数学进展
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157842]
专题	数学科学学院
推荐引用方式 GB/T 7714	Jin, Xian&apos,Zhang, Fuji,an. The replacements of signed graphs and Kauffman brackets of link families. 2007-01-01.

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