Abstract:
Knot theory is the branch of algebraic topology. A knot is considered as the embed ding of a unit circle in R
3
. 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.
