The Link Component Number of Suspended Trees

This paper provides a relationship between a geometric structure of a suspended tree and the number of link components of the associated link diagram.Comment: 7 pages, 5 figure

Musubime to karamime no gurafu hyogen

制度:新 ; 報告番号:乙2277号 ; 学位の種類:博士(理学) ; 授与年月日:2010/6/22 ; 早大学位記番号:新540

The computation of k-defect polynomials, suspended Y -trees and its applications

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.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