Cayley graphs and coverings

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Julia Lazenby, Allison Davis, Taylor Coon, and Joe Consiglio

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Table of contents

1 Works based on this project 1.1 Rose-Hulman Electronic Journal 1.2 Abstracts for talks given at the Young Mathematicians Conference 2 Information related to this project 2.1 Cayley graphs and coverings 2.2 Finite Graphs 2.3 The figure equation 2.4 Transformations of graphs, characteristic polynomials, and spectra 2.5 Graphs coming from the symmetries of the cube

Works based on this project

Rose-Hulman Electronic Journal

• Taylor Coon's paper can be found at Rose-Hulman Vol. 7 #2 (http://www.rose-hulman.edu/mathjournal/v7n2.php).

Abstracts for talks given at the Young Mathematicians Conference

• Cayley graphs of finite abelian groups by Julia Lazenby
• Transformations of graphs, characteristic polynomials, and spectra by Allison Davis
• A family of graphs coming from the symmetries of the cube by Joseph Consiglio
• Combinatorics of the Figure Equation on directed graphs by Taylor Coon

Information related to this project

Cayley graphs and coverings

• Cayley graphs and coverings Definitions
• Interlacing and hamiltonian circuits
• Theorems about Cayley graphs and coverings
• Characteristic Polynomials of Cayley Graphs of the Symmetric Group
• Multiplying Cayley graphs of cyclic groups
• Spectrum of Cayley graphs of cyclic groups

Finite Graphs

• Theorems about finite graphs

The figure equation

• Figure Equation
• The Figure Equation - Main Results

Transformations of graphs, characteristic polynomials, and spectra

• Adding loops
• Doubling edges
• Products of Graphs
• Powers
• Edge Reversal

Graphs coming from the symmetries of the cube

• Action graphs for symmetries of the cube