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 deletioncontraction 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.
Subjects  Engineering 

Journal Section  Articles 
Authors 

Bibtex  @research article { cbayarfbe323841,
journal = {Celal Bayar University Journal of Science},
issn = {1305130X},
eissn = {13051385},
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), 929932. 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): 929932 <http://dergipark.org.tr/cbayarfbe/issue/33464/323841> 
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): 929932 
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  1305130X13051385 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 1305130X13051385 %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): 929932. https://doi.org/10.18466/cbayarfbe.323841 