ISOPERIMETRIC CONSTANTS IN PLANAR GRAPHS WITH HYPERBOLIC PROPERTIES

dc.contributor.advisorZha, Xiaoyaen_US
dc.contributor.authorWhitlatch, Hays Wimsatten_US
dc.contributor.committeememberHart, Jamesen_US
dc.contributor.committeememberNelson, Donen_US
dc.contributor.committeememberStephens, Chrisen_US
dc.contributor.committeememberYe, Dongen_US
dc.contributor.departmentBasic & Applied Sciencesen_US
dc.date.accessioned2014-06-02T19:01:52Z
dc.date.available2014-06-02T19:01:52Z
dc.date.issued2014-05-25en_US
dc.description.abstractIsoperimetric inequalities date back to ancient Greece where figures with equal perimeters but different shapes were compared (Zenodorus, On Isoperimetric Figures). The original problem was to maximize the area contained within a curve of specified length. In Euclidean geometry the result is a circle. This can be generalized to shapes on non-Euclidean surfaces as well as for higher dimensions where we seek to maximize the hyperdimensional volume respective to the hyperdimensional surface area.en_US
dc.description.abstracten_US
dc.description.abstractThe subject of this thesis is isoperimetric constants in planar graphs with hyperbolic properties. We first analyze isoperimetric constants in the flat plane which has curvature 0 and then give an overview of two isoperimetric constants that give a hyperbolicity criterion for infinite vertex-regular, face-regular planar graphs. Finally we extend the concept to general planar graphs with hyperbolic properties and establish that the same constants serve as a lower bound.en_US
dc.description.degreeM.S.en_US
dc.identifier.urihttp://jewlscholar.mtsu.edu/handle/mtsu/3625
dc.publisherMiddle Tennessee State Universityen_US
dc.subject.umiMathematicsen_US
dc.thesis.degreegrantorMiddle Tennessee State Universityen_US
dc.thesis.degreelevelMastersen_US
dc.titleISOPERIMETRIC CONSTANTS IN PLANAR GRAPHS WITH HYPERBOLIC PROPERTIESen_US
dc.typeThesisen_US

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