Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 5, Issue 2


Published
on

December 31, 2020


Pages

397-402


DOI

Article

Dichromatic polynomial for graph of a (2,n)-torus knot

Check for updates


Authors

Abdulgani Şahin Affiliation:
Department of Mathematics, Faculty of Science and Letters, Ağrı İbrahim Çeçen University, 04100, Ağrı, Turkey


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

Published by: Engineering Journals

Engineering Journals Logo