Werner, Simon2015-02-062015-02-062015-02-06http://hdl.handle.net/10539/16917A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfilment of requirements for the degree of Master of Science. June 2014.We start by defining a class of graphs called the suspended Y -trees and give some of its properties. We then classify all the closed sets of a general suspended Y -tree. This will lead us to counting the graph compositions of the suspended Y -tree. We then contract these closed sets one by one to obtain a set of minors for the suspended Y -trees. We will use this information to compute some of the general expression of the k-defect polynomial of a suspended Y -tree. Finally we compute the explicit Tutte polynomial of the suspended Y -trees.enPolynomials.The computation of k-defect polynomials, suspended Y -trees and its applicationsThesis