Polynomial Invariants Of Knots

Abstract

Knot theory is the branch of algebraic topology. A knot is considered as the embed ding of a unit circle in R3. Polynomial knot invariants play a vital role to understand underlying aspects of knotted structures. Tutte polynomial provides many combina torial properties for knots. In this thesis we study the Tutte polynomial by associating directed planar multi graphs with knotted structures. We compute Tutte polynomial for (2,n) torus knots and Dn k family of knots. For (2,n) torus knots and Dn k family of knots we also compute number of spanning trees and chromatic polynomial which are the combinatorial properties of Tutte polynomial.