Tutte Polynomial for Graphs of Twist Knots

Year 2018, Volume: 10, 61 - 66, 29.12.2018

Abdulgani Şahin , Bünyamin Şahin

Abstract

The Tutte polynomial is a two-variable polynomial that is connected by a graph, a matroid or a matrix.

The Tutte polynomial has a lot of exciting applications in dierent areas for example combinatorics, probability,

knot theory, algebra, statistical mechanics, computer sciences, chemistry and biology. It was indicated by W. T.

Tutte. We transport the Tutte polynomial to knot theory. Because each knot have a corresponding graph. We

study the Tutte polynomial for graphs of twist knots. We find some general forms for the Tutte polynomial of

graphs belonging to twist knots and the Tutte polynomial of signed graphs belonging to twist knots. Twist knots

are significant class of knots to take into account especially in contact geometry.

Keywords

Twist knots, Knot graph, Tutte polynomial, Signed graph

References

• Bollobas, B., Modern Graph Theory, Springer Science + Business Media, Inc, New York, 1998.
• Haggard, G., Pearce, D.J., Royle, G., Computing Tutte polynomials, ACM Transactions on Mathematical Software, 37(3)(2010), Article Number:24.
• Johnson, I., Henrich, A.K., A Interactive Introduction to Knot Theory, Dover Publications, Inc., Mineola, New York, 2017.
• Kauman, L.H., A Tutte polynomial for signed graphs, Discrete Applied Mathematics, 25(1989), 105–127.