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## The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots

#### Abdulgani̇ Şahi̇n [1] , Abdullah Kopuzlu [2]

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In knot theory there are many important invariants that are hard to calculate. They are classified as numeric, group and polynomial invariants. These invariants contribute to the problem of classification of knots. In this study, we have done a study on the polynomial invariants of the knots. First of all, for (2,n)-torus knots which is a special class of knots, we calculated their the Kauffman bracket polynomials. We have found a general formula for these calculations. Then the Tutte polynomials of signed graphs of (2,n)-torus knots, marked with a {+} or {-} sign each on edge, have been computed. Some results have been obtained at the end of these calculations. While these researches have been studied, figures and regular diagrams of knots have been applied so much. During the first calculation, we have used skein diagrams and relations of the Kauffman polynomial. In the second calculation, the Tutte polynomials of (2,n)-torus knots have been computed and at the end of the operation some general formulas have been introduced. The signed graphs of (2,n)-torus knots have been obtained by using their regular diagrams. Then the Tutte polynomials of these graphs have been computed as a diagrammatic by recursive formulas that can be defined by deletion-contraction operations. Finally, it has been obtained that there is a relation between the Tutte polynomials and the Kauffman bracket polynomials of (2,n)-torus knots.

Kauffman polynomial, Knots, Knot graph, Torus knots
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Subjects Engineering Articles Author: Abdulgani̇ Şahi̇nCountry: Turkey Author: Abdullah KopuzluCountry: Turkey
 Bibtex @research article { cbayarfbe323841, journal = {Celal Bayar University Journal of Science}, issn = {1305-130X}, eissn = {1305-1385}, address = {Celal Bayar University}, year = {2017}, volume = {13}, pages = {929 - 932}, doi = {10.18466/cbayarfbe.323841}, title = {The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots}, key = {cite}, author = {Şahi̇n, Abdulgani̇ and Kopuzlu, Abdullah} } APA Şahi̇n, A , Kopuzlu, A . (2017). The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots. Celal Bayar University Journal of Science, 13 (4), 929-932. DOI: 10.18466/cbayarfbe.323841 MLA Şahi̇n, A , Kopuzlu, A . "The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots". Celal Bayar University Journal of Science 13 (2017): 929-932 Chicago Şahi̇n, A , Kopuzlu, A . "The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots". Celal Bayar University Journal of Science 13 (2017): 929-932 RIS TY - JOUR T1 - The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots AU - Abdulgani̇ Şahi̇n , Abdullah Kopuzlu Y1 - 2017 PY - 2017 N1 - doi: 10.18466/cbayarfbe.323841 DO - 10.18466/cbayarfbe.323841 T2 - Celal Bayar University Journal of Science JF - Journal JO - JOR SP - 929 EP - 932 VL - 13 IS - 4 SN - 1305-130X-1305-1385 M3 - doi: 10.18466/cbayarfbe.323841 UR - https://doi.org/10.18466/cbayarfbe.323841 Y2 - 2017 ER - EndNote %0 Celal Bayar University Journal of Science The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots %A Abdulgani̇ Şahi̇n , Abdullah Kopuzlu %T The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots %D 2017 %J Celal Bayar University Journal of Science %P 1305-130X-1305-1385 %V 13 %N 4 %R doi: 10.18466/cbayarfbe.323841 %U 10.18466/cbayarfbe.323841 ISNAD Şahi̇n, Abdulgani̇ , Kopuzlu, Abdullah . "The Relationship Between The Kauffman Bracket Polynomials and The Tutte Polynomials of (2,n)-Torus Knots". Celal Bayar University Journal of Science 13 / 4 (December 2017): 929-932. https://doi.org/10.18466/cbayarfbe.323841