Article
Dichromatic polynomial for graph of a (2,n)-torus knot
Authors
Abstract
In this study, we introduce the relationship between the Tutte polynomials and dichromatic polynomials of (2,n)-torus knots. For this aim, firstly we obtain the signed graph of a (2,n)-torus knot, marked with {+} signs, via the regular diagram of its. Whereupon, we compute the Tutte polynomial for this graph and find a generalization through these calculations. Finally we obtain dichromatic polynomial lying under the unmarked states of the signed graph of the (2,n)-torus knots by the generalization.
Keywords
Knot, knot graph, Tutte polynomial, dichromatic polynomial, signed graph, 57M15, 57M25, 57M27
Citation
Şahin, A. (2020). Dichromatic polynomial for graph of a (2,n)-torus knot. Applied Mathematics and Nonlinear Sciences, 5(2), 397–402. https://doi.org/10.2478/amns.2020.2.00068
A. Şahin, “Dichromatic polynomial for graph of a (2,n)-torus knot,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, pp. 397–402, 2020, doi: 10.2478/amns.2020.2.00068.
Şahin A. Dichromatic polynomial for graph of a (2,n)-torus knot. Applied Mathematics and Nonlinear Sciences. 2020;5(2):397–402. doi:10.2478/amns.2020.2.00068.
Şahin, A. (2020), ‘Dichromatic polynomial for graph of a (2,n)-torus knot’, Applied Mathematics and Nonlinear Sciences, 5(2), pp. 397–402. Available at: https://doi.org/10.2478/amns.2020.2.00068.
Şahin, Abdulgani. “Dichromatic Polynomial for Graph of a (2,n)-torus Knot.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, 2020, pp. 397–402. https://doi.org/10.2478/amns.2020.2.00068.
Şahin, Abdulgani. “Dichromatic Polynomial for Graph of a (2,n)-torus Knot.” Applied Mathematics and Nonlinear Sciences 5, no. 2 (2020): 397–402. https://doi.org/10.2478/amns.2020.2.00068.
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Published by: Engineering Journals


