The main result in this thesis bounds the combinatorial modulus of a ring in a triangulation graph in terms of the modulus of a related ring. The bounds depend only on how the rings are related and not on the rings themselves. This may be used to solve the combinatorial type problem in a variety of situation, most significant in graphs with unbounded degree. Other results regarding the type problem are presented along with several examples illustrating the limits of the results. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of
the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2006. / Date of Defense: July 6, 2006. / Graph Theory, Circle Packing, Discrete Conformal Geometry, Conformal Type / Includes bibliographical references. / Philip Bowers, Professor Directing Dissertation; Lois Hawkes, Outside Committee Member; Steve Bellenot, Committee Member; Eric Klassen, Committee Member; Craig Nolder, Committee Member; Jack Quine, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_168961 |
| Contributors | Wood, William E. (authoraut), Bowers, Philip (professor directing dissertation), Hawkes, Lois (outside committee member), Bellenot, Steve (committee member), Klassen, Eric (committee member), Nolder, Craig (committee member), Quine, Jack (committee member), Department of Mathematics (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
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