The computation of k-defect polynomials, suspended Y -trees and its applications
Date
2015-02-06
Authors
Werner, Simon
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Abstract
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.
Description
A 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.