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    An exploration of two infinite families of snarks

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    Author
    Ver Hoef, Lander
    Chair
    Berman, Leah
    Committee
    Williams, Gordon
    Faudree, Jill
    Keyword
    Petersen graphs
    graph theory
    graph coloring
    graph connectivity
    Metadata
    Show full item record
    URI
    http://hdl.handle.net/11122/10547
    Abstract
    In this paper, we generalize a single example of a snark that admits a drawing with even rotational symmetry into two infinite families using a voltage graph construction techniques derived from cyclic Pseudo-Loupekine snarks. We expose an enforced chirality in coloring the underlying 5-pole that generated the known example, and use this fact to show that the infinite families are in fact snarks. We explore the construction of these families in terms of the blowup construction. We show that a graph in either family with rotational symmetry of order m has automorphism group of order m2m⁺¹. The oddness of graphs in both families is determined exactly, and shown to increase linearly with the order of rotational symmetry.
    Description
    Thesis (M.S.) University of Alaska Fairbanks, 2019
    Table of Contents
    Chapter 1: Introduction -- 1.1 General Graph Theory -- Chapter 2: Introduction to Snarks -- 2.1 History -- 2.2 Motivation -- 2.3 Loupekine Snarks and k-poles -- 2.4 Conditions on Triviality -- Chapter 3: The Construction of Two Families of Snarks -- 3.1 Voltage Graphs and Lifts -- 3.2 The Family of Snarks, Fm -- 3.3 A Second Family of Snarks, Rm -- Chapter 4: Results -- 4.1 Proof that the graphs Fm and Rm are Snarks -- 4.2 Interpreting Fm and Rm as Blowup Graphs -- 4.3 Automorphism Group -- 4.4 Oddness -- Chapter 5: Conclusions and Open Questions -- References.
    Date
    2019-05
    Type
    Thesis
    Collections
    Mathematics and Statistics

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