Posts Tagged ‘ cubic graph ’

Thesis Draft 5

From here on, each draft of my thesis will be constructed using PCTeX.

Thesis Draft 5


Thesis Draft 4 (PCTeX)

Dr. Sharma asked me to rewrite what I had so far for my thesis using PCTeX. PCTeX is a software that uses TeX, a mathematical language, to produce documents. I have been learning the software and language as I go, so these drafts are truly works in progress.

Thesis Draft 4 (PCTeX)

Thesis Draft 3

This draft reflects the new organization of my thesis and main topics we aim to cover. Some of the topics have already been discussed, but I did not have time to add them to this draft of the paper. See blog posts for up-to-date information on what topics I have already researched.

Thesis Draft 3

LCF Notation

I’m doing some research on LCF notation to see how it relates mathematics to chemistry. LCF notation was originally developed by Joshua Lederberg as a way to represent cyclic graphs in chemistry. It was further developed by Coxeter and Frucht, who dubbed the notation LCF. Here is the original paper written by Lederberg that first uses the notation.

Lederberg Paper

Thesis Draft 2: Examples and LCF Notation

After meeting with my adviser, he suggested some changes for my terminology section and added some new sections. I have now also included personal examples of cubic graphs that I have drawn and LCF notation.

Thesis Draft 2: Examples and LCF Notation

Thesis Draft 1: Terminology and Known Cubic Cages

I have begun to type up the beginning stages of my thesis, even though we have not completely defined it’s format. I know it will be focussed on the study of cubic graphs and their applications, so my adviser asked me to type up the terminology and known cubic cages sections to start with. I will be including drafts frequently as we add and change material.

Thesis Draft 1: Terminology and Known Cages

LCF Notation for 3-6 Graphs on 14, 16, and 18 Vertices

Tuesday I learned how to express Hamiltonian graphs in LCF notation. LCF notation begins with a Hamiltonian graph. From there, it shows you how to draw a cubic graph by starting at any vertex. Below is the LCF notation for the 3-6 graphs I have drawn on 14, 16, and 18 vertices.

3-6 Cage
LCF Notation [ 5, -5]^7

3-6 Cage

 3-6 Graph on 16 Vertices
LCF Notation [5, -5, 6, -5, 6, -5, 5, 6, -6, 6, -6, -5, 5, -6, 5, -6]

 3-6 Graph on 18 Vertices
LCF Notation [5, 9, -5]^6

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