The replacements of signed graphs and Kauffman brackets of links
| dc.creator | Jin, Xian'an | |
| dc.creator | Zhang, Fuji | |
| dc.date | 2005-11-13 | |
| dc.date.accessioned | 2026-07-07T06:51:11Z | |
| dc.date.available | 2026-07-07T06:51:11Z | |
| dc.description | Let $G$ be a signed graph. Let $\hat{G}$ be the graph obtained from $G$ by replacing each edge $e$ by a chain or a sheaf. We first establish a relation between the $Q$-polynomial of $\hat{G}$[6] and the $W$-polynomial of $G$ [9]. Two special dual cases are derived from the relation, one of which has been studied in [8]. Based on the one to one correspondence between signed plane graphs and link diagrams, and the correspondence between the $Q$-polynomial of signed plane graph and the Kauffman bracket of link diagram, we can compute the Kauffman bracket of link diagram corresponding to $\hat{G}$ by means of the $W$-polynomial of $G$. By this way we use transfer matrix approach to compute the Kauffman bracket of rational links, and obtain their closed-form formulae. Finally we provide an example to point out that the relation we built can be used to deal with a wide type of link family. | |
| dc.description | 18 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0511326 | |
| dc.identifier | http://arxiv.org/abs/math/0511326 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104904 | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M15 | |
| dc.title | The replacements of signed graphs and Kauffman brackets of links | |
| dc.type | text |