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Discrete Mathematics and Combinatorics

2015

ETD

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Full-Text Articles in Mathematics

Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman Jan 2015

Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman

Electronic Theses and Dissertations

In this thesis, we examine two topics. In the first part, we consider Leech tree which is a tree of order n with positive integer edge weights such that the weighted distances between pairs of vertices are exactly from 1 to n choose 2. Only five Leech trees are known and some non-existence results have been presented through the years. Variations of Leech trees such as the minimal distinct distance trees and modular Leech trees have been considered in recent years. In this thesis, such Leech-type questions on distances between leaves are studied as well as some other labeling questions …


Graphs Of Classroom Networks, Rebecca Holliday Jan 2015

Graphs Of Classroom Networks, Rebecca Holliday

Electronic Theses and Dissertations

In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism …