Triangulated ladders, polynomials and links.

Abstract

In this thesis we study three graph polynomials, namely, the chromatic polynomial, the Tutte polynomial and the coboundary polynomial. We define a class of graphs which we call triangulated ladder and give some of its properties. Then we find an explicit expression of the chromatic polynomial for this class of graphs. Furthermore, we find a recursive expression of the Tutte polynomial and a recursive expression of the coboundary polynomial for this class of graphs. Finally we give a class of links associated with triangulated ladders and give some of their properties.