{"id":{"repo_id":"unt","oai_identifier":"info:ark/67531/metadc2545"},"canonical_url":"https://search.dev.ndltd.org/etd/unt/info:ark/67531/metadc2545","repository":{"repo_id":"unt","name":"University of North Texas","base_url":"https://digital.library.unt.edu/oai/"},"display":{"title":"Infinite Planar Graphs","abstract":"How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism.","abstract_html":"How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism.","abstract_has_math":false,"creators":["Aurand, Eric William"],"institution":"University of North Texas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Brand, Neal","Kung, Joseph","Monticino, Michael G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2000,"date_issued":"2000-05","date_published":"2000-05","updated_at":"2026-07-24T05:34:52Z","subjects":["Graph theory.","Geodesics (Mathematics)","Automorphisms.","equivalence classes","excess of a vertex","planar graph","geodesic ray","automorphism"],"languages":["English"],"rights":["Public","Copyright","Aurand, Eric William","Copyright is held by the author, unless otherwise noted. 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The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism."]},{"key":"dc:format","label":"Dc Format","values":["Text"]},{"key":"dc:title","label":"Title","values":["Infinite Planar Graphs"]}]}],"canonical_facts":{"dc:contributor":["Brand, Neal","Kung, Joseph","Monticino, Michael G."],"dc:creator":["Aurand, Eric William"],"dc:date":["2000-05"],"dc:description":["How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism."],"dc:format":["Text"],"dc:identifier":["oclc: 47144615","untcat: b2300272","doi: 10.12794/metadc2545","https://digital.library.unt.edu/ark:/67531/metadc2545/","ark: ark:/67531/metadc2545"],"dc:language":["English"],"dc:publisher":["University of North Texas"],"dc:rights":["Public","Copyright","Aurand, Eric William","Copyright is held by the author, unless otherwise noted. All rights reserved."],"dc:subject":["Graph theory.","Geodesics (Mathematics)","Automorphisms.","equivalence classes","excess of a vertex","planar graph","geodesic ray","automorphism"],"dc:title":["Infinite Planar Graphs"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:34:52Z"}