An exploration of two infinite families of snarks

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Show simple item record Ver Hoef, Lander 2019-07-07T18:52:55Z 2019-07-07T18:52:55Z 2019-05
dc.description Thesis (M.S.) University of Alaska Fairbanks, 2019 en_US
dc.description.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. en_US
dc.description.tableofcontents 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. en_US
dc.language.iso en_US en_US
dc.subject Petersen graphs en_US
dc.subject graph theory en_US
dc.subject graph coloring en_US
dc.subject graph connectivity en_US
dc.title An exploration of two infinite families of snarks en_US
dc.type Thesis en_US ms en_US
dc.identifier.department Department of Mathematics en_US
dc.contributor.chair Berman, Leah
dc.contributor.committee Williams, Gordon
dc.contributor.committee Faudree, Jill

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