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dc.contributor.authorVer Hoef, Lander
dc.date.accessioned2019-07-07T18:52:55Z
dc.date.available2019-07-07T18:52:55Z
dc.date.issued2019-05
dc.identifier.urihttp://hdl.handle.net/11122/10547
dc.descriptionThesis (M.S.) University of Alaska Fairbanks, 2019en_US
dc.description.abstractIn 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.en_US
dc.description.tableofcontentsChapter 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.en_US
dc.language.isoen_USen_US
dc.subjectPetersen graphsen_US
dc.subjectgraph theoryen_US
dc.subjectgraph coloringen_US
dc.subjectgraph connectivityen_US
dc.titleAn exploration of two infinite families of snarksen_US
dc.typeThesisen_US
dc.type.degreemsen_US
dc.identifier.departmentDepartment of Mathematicsen_US
dc.contributor.chairBerman, Leah
dc.contributor.committeeWilliams, Gordon
dc.contributor.committeeFaudree, Jill
refterms.dateFOA2020-03-06T02:55:31Z


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