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Theses Digitization Project

Theses/Dissertations

Graph theory

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The Fibonacci Sequence And Hosoya's Triangle, Jeffrey Lee Smith Jan 2013

The Fibonacci Sequence And Hosoya's Triangle, Jeffrey Lee Smith

Theses Digitization Project

The purpose of this thesis is to study the Fibonacci sequence in a context many are unfamiliar with. A triangular array of numbers, similar looking to Pascal's triangle, was constructed a few decades ago and is called Hosoya's triangle. Each element within the triangle is created using Fibonacci numbers.


Whitney's 2-Isomorphism Theorem For Hypergraphs, Eric Anthony Taylor Jan 2013

Whitney's 2-Isomorphism Theorem For Hypergraphs, Eric Anthony Taylor

Theses Digitization Project

This study will examine a fundamental theorem from graph theory: Whitney's 2-Isomorphism Theorem. Whitney's 2-Isomorphism theorem characterizes when two graphs have isomorphic cycle matroids.


A Study Of Finite Symmetrical Groups, Patrick Kevin Martinez Jan 2013

A Study Of Finite Symmetrical Groups, Patrick Kevin Martinez

Theses Digitization Project

This study discovered several important groups that involve the classical and sporadic groups. These groups appeared as finite homomorphic images of the progenitors 3*8 : PGL₂(7), 2*¹⁴ : L₃ (2), 5*³ : S₃ and 7*2 : m S₃.


Prouhet-Tarry-Escott Problem, Juan Manuel Gutierrez Jan 2012

Prouhet-Tarry-Escott Problem, Juan Manuel Gutierrez

Theses Digitization Project

The purpose of this research paper is to gain a deeper understanding of a famous unsolved mathematical problem known as the Prouhet-Terry-Escott Problem. The Prouhet-Terry-Escott Problem is a complex problem that still has much to be discovered. This fascinating problem shows up in many areas of mathematics such as the study of polynomials, graph theory, and the theory of integral quadratic forms.


Snort: A Combinatorial Game, Keiko Kakihara Jan 2010

Snort: A Combinatorial Game, Keiko Kakihara

Theses Digitization Project

This paper focuses on the game Snort, which is a combinatorial game on graphs. This paper will explore the characteristics of opposability through examples. More fully, we obtain some neccessary conditions for a graph to be opposable. Since an opposable graph guarantees a second player win, we examine graphs that result in a first player win.


Tutte Polynomial In Knot Theory, David Alan Petersen Jan 2007

Tutte Polynomial In Knot Theory, David Alan Petersen

Theses Digitization Project

This thesis reviews the history of knot theory with an emphasis on the diagrammatic approach to studying knots. Also covered are the basic concepts and notions of graph theory and how these two fields are related with an example of a knot diagram and how to associate it to a graph.


Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez Jan 2006

Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez

Theses Digitization Project

A 2004 article written by Yixun Lin and Aifeng Yang published in the journal Discrete Math characterized the set of a 3-cutwidth critical graphs by five specified elements. This project extends the idea to 4-cutwidth critical graphs.


Various Steiner Systems, Valentin Jean Racataian Jan 2004

Various Steiner Systems, Valentin Jean Racataian

Theses Digitization Project

This project deals with the automorphism group G of a Steiner system S (3, 4, 10). S₁₀, the symmetrical group of degree 10, acts transitively on T, the set of all Steiner systems with parameters 3, 4, 10. The purpose of this project is to study the action of S₁₀ on cosets of G. This will be achieved by means of a graph of S₁₀ on T x T. The orbits of S₁₀ on T x T are in one-one correspondence with the orbits of G, the stabilizer of an S [e] T on T.


The Embedding Of Complete Bipartite Graphs Onto Grids With A Minimum Grid Cutwidth, Mário Rocha Jan 2003

The Embedding Of Complete Bipartite Graphs Onto Grids With A Minimum Grid Cutwidth, Mário Rocha

Theses Digitization Project

Algorithms will be domonstrated for how to embed complete bipartite graphs onto 2xn type grids, where the imimum grid cutwidth is attained.


The Edge-Isoperimetric Problem For The Square Tessellation Of Plane, Sunmi Lee Jan 2000

The Edge-Isoperimetric Problem For The Square Tessellation Of Plane, Sunmi Lee

Theses Digitization Project

The solution for the edge-isoperimetric problem (EIP) of the square tessellation of plane is investigated and solved. Summaries of the stabilization theory and previous research dealing with the EIP are stated. These techniques enable us to solve the EIP of the cubical tessellation.


Solutions To The Chinese Postman Problem, Kenneth Peter Cramm Jan 2000

Solutions To The Chinese Postman Problem, Kenneth Peter Cramm

Theses Digitization Project

Considering the Chinese Postman Problem, in which a mailman must deliver mail to houses in a neighborhood. The mailman must cover each side of the street that has houses, at least once. The focus of this paper is our attempt to discover the optimal path, or the least number of times each street is walked. The integration of algorithms from graph theory and operations research form the method used to explain solutions to the Chinese Postman Problem.