{"id":{"repo_id":"mississippi","oai_identifier":"oai:egrove.olemiss.edu:etd-2323"},"canonical_url":"https://search.dev.ndltd.org/etd/mississippi/oai:egrove.olemiss.edu:etd-2323","repository":{"repo_id":"mississippi","name":"University of Mississippi","base_url":"https://egrove.olemiss.edu/do/oai/"},"display":{"title":"Bipartite Density of Generalized Petersen Graphs","abstract":"The bipartite density b(G) of a graph G with m edges is the maximum ratio [special characters omitted] where m0 is the number of edges in a bipartitesubgraph of G. In this study we determine the bipartite density of several classes of Generalized Petersen Graphs. These graphs are denoted by P(n, k), where n ≥ 3 and 1 ≤ k < n with n ≠ 2k. The Generalized Petersen Graph P(n, k) has vertices [special characters omitted] and edges [special characters omitted] where subscript addition is modulo n. We define subgraphs P'(n, k) of P( n, k) by deleting the edge vn –1v0 and the edges w iwi+k for n – k ≤ i ≤ n – 1. For P'(n, k) and many classes of P(n, k), we determine the exact number of edges which must be removed from P( n, k) to reduce it to a bipartite subgraph. In many classes of Generalized Petersen Graphs the exact bipartite density is derived. For example: b(P(n, k)) = 1 for n even, k odd; b(P(n, k)) = 1 – [special characters omitted] for n and k odd and n > k²; b(P( n, k)) is asymptotically 1 – [special characters omitted] for n odd, k even.","abstract_html":"The bipartite density b(G) of a graph G with m edges is the maximum ratio [special characters omitted] where m0 is the number of edges in a bipartitesubgraph of G. In this study we determine the bipartite density of several classes of Generalized Petersen Graphs. These graphs are denoted by P(n, k), where n ≥ 3 and 1 ≤ k &lt; n with n ≠ 2k. The Generalized Petersen Graph P(n, k) has vertices [special characters omitted] and edges [special characters omitted] where subscript addition is modulo n. We define subgraphs P&#x27;(n, k) of P( n, k) by deleting the edge vn –1v0 and the edges w iwi+k for n – k ≤ i ≤ n – 1. For P&#x27;(n, k) and many classes of P(n, k), we determine the exact number of edges which must be removed from P( n, k) to reduce it to a bipartite subgraph. In many classes of Generalized Petersen Graphs the exact bipartite density is derived. For example: b(P(n, k)) = 1 for n even, k odd; b(P(n, k)) = 1 – [special characters omitted] for n and k odd and n &gt; k²; b(P( n, k)) is asymptotically 1 – [special characters omitted] for n odd, k even.","abstract_has_math":false,"creators":["Ewell, Lisa Jordan"],"institution":null,"degree_name":"M.S. in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["William Staton","Micah B. Milinovich","Talmadge James Reid"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T03:06:44Z","subjects":["Bipartite Density","Generalized Petersen Graphs","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://egrove.olemiss.edu/etd/1324","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["William Staton","Micah B. Milinovich","Talmadge James Reid"]},{"key":"dc:creator","label":"Author","values":["Ewell, Lisa Jordan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2020-01-23T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S. in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Bipartite Density","Generalized Petersen Graphs","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://egrove.olemiss.edu/etd/1324"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The bipartite density b(G) of a graph G with m edges is the maximum ratio [special characters omitted] where m0 is the number of edges in a bipartitesubgraph of G. In this study we determine the bipartite density of several classes of Generalized Petersen Graphs. These graphs are denoted by P(n, k), where n ≥ 3 and 1 ≤ k < n with n ≠ 2k. The Generalized Petersen Graph P(n, k) has vertices [special characters omitted] and edges [special characters omitted] where subscript addition is modulo n. We define subgraphs P'(n, k) of P( n, k) by deleting the edge vn –1v0 and the edges w iwi+k for n – k ≤ i ≤ n – 1. For P'(n, k) and many classes of P(n, k), we determine the exact number of edges which must be removed from P( n, k) to reduce it to a bipartite subgraph. In many classes of Generalized Petersen Graphs the exact bipartite density is derived. For example: b(P(n, k)) = 1 for n even, k odd; b(P(n, k)) = 1 – [special characters omitted] for n and k odd and n > k²; b(P( n, k)) is asymptotically 1 – [special characters omitted] for n odd, k even."]},{"key":"dc:title","label":"Title","values":["Bipartite Density of Generalized Petersen Graphs"]}]}],"canonical_facts":{"dc:contributor":["William Staton","Micah B. Milinovich","Talmadge James Reid"],"dc:creator":["Ewell, Lisa Jordan"],"dc:date.available":["2020-01-23T08:00:00Z"],"dc:description.abstract":["The bipartite density b(G) of a graph G with m edges is the maximum ratio [special characters omitted] where m0 is the number of edges in a bipartitesubgraph of G. In this study we determine the bipartite density of several classes of Generalized Petersen Graphs. These graphs are denoted by P(n, k), where n ≥ 3 and 1 ≤ k < n with n ≠ 2k. The Generalized Petersen Graph P(n, k) has vertices [special characters omitted] and edges [special characters omitted] where subscript addition is modulo n. We define subgraphs P'(n, k) of P( n, k) by deleting the edge vn –1v0 and the edges w iwi+k for n – k ≤ i ≤ n – 1. For P'(n, k) and many classes of P(n, k), we determine the exact number of edges which must be removed from P( n, k) to reduce it to a bipartite subgraph. In many classes of Generalized Petersen Graphs the exact bipartite density is derived. For example: b(P(n, k)) = 1 for n even, k odd; b(P(n, k)) = 1 – [special characters omitted] for n and k odd and n > k²; b(P( n, k)) is asymptotically 1 – [special characters omitted] for n odd, k even."],"dc:identifier":["https://egrove.olemiss.edu/etd/1324"],"dc:subject":["Bipartite Density","Generalized Petersen Graphs","Mathematics"],"dc:title":["Bipartite Density of Generalized Petersen Graphs"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S. in Mathematics"]},"updated_at":"2026-07-24T03:06:44Z"}