A bracket polynomial for graphs, III. Vertex weights
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Abstract
- In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e. looped graphs whose vertices have been partitioned into two classes (marked and not marked). The marked-graph bracket polynomial is readily modified to handle graphs with weighted vertices. We present formulas that simplify the computation of this weighted bracket for graphs that contain twin vertices or are constructed using graph composition, and we show that graph composition corresponds to the construction of a link diagram from tangles.
| Title | A bracket polynomial for graphs, III. Vertex weights |
|---|---|
| Creator | Traldi, Lorenzo |
| Publisher | Journal of Knot Theory and Its Ramifications |
| Academic Department | Mathematics |
| Division | Natural Sciences |
| Organization | Lafayette College |
| Date Issued | March 2011 |
| Date Available | 2015-05-06T17:31:45Z |
| Type | Article |
| Language | English |
| Keyword | graph composition |
| graph | |
| Kauffman bracket | |
| twin vertex | |
| parallel | |
| series | |
| vertex weight | |
| tangle | |
| virtual link | |
| Bibliographic Citation | Traldi, L. (2011 Mar.) "A bracket polynomial for graphs, III. Vertex weights." Journal of Knot Theory and Its Ramifications |
| Standard Identifier | Handle 10385/1872 |
| DOI DOI: 10.1142/S0218216511008875 | |
| Permalink | http://hdl.handle.net/10385/1872 |
| Rights Statement |
In Copyright
|
| Rights Holders | World Scientific Publishing Company |
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| File | Traldi-JournalofKnotTheoryandItsRamifications-vol20-no3-2011.pdf | Uploaded 2019-10-20 | Public | Download |
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