In the study of triple systems, one question faced is that of finding for what order a decomposition exists. We state and prove a necessary and sufficient condition for the existence of a bicyclic mixed triple system based on the three possible partial orientations of the 3-cycle with twice as many arcs as edges. We also explore the existence of rotational and reverse mixed triple systems. Our principal proof technique applied is the difference method. Finally, this work contains a result on packing of complete mixed graphs on v vertices, Mv, with isomorphic copies of two of the mixed triples and a possible leave structure.
","abstract_html":"<p>In the study of triple systems, one question faced is that of finding for what order a decomposition exists. We state and prove a necessary and sufficient condition for the existence of a <em>bicyclic mixed triple system</em> based on the three possible partial orientations of the 3-cycle with twice as many arcs as edges. We also explore the existence of <em>rotational</em> and <em>reverse mixed triple systems</em>. Our principal proof technique applied is the <em>difference method</em>. Finally, this work contains a result on <em>packing</em> of <em>complete mixed graphs</em> on <em>v</em> vertices, <em>M<sub>v</sub></em>, with isomorphic copies of two of the mixed triples and a possible <em>leave</em> structure.</p>","abstract_has_math":false,"creators":["Bobga, Benkam Benedict"],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-08-16T07:00:00Z","date_published":"2005-08-16T07:00:00Z","updated_at":"2026-07-24T02:19:43Z","subjects":["difference triples","packings","automorphisms","reverse triples","triple systems","mixed graphs","rotational","bicyclic","Applied Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1043","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Bobga, Benkam Benedict"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2005-08-16T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["difference triples","packings","automorphisms","reverse triples","triple systems","mixed graphs","rotational","bicyclic","Applied Mathematics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/2200/viewcontent/BobgaB072805f.pdf","https://dc.etsu.edu/etd/1043"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In the study of triple systems, one question faced is that of finding for what order a decomposition exists. We state and prove a necessary and sufficient condition for the existence of a bicyclic mixed triple system based on the three possible partial orientations of the 3-cycle with twice as many arcs as edges. We also explore the existence of rotational and reverse mixed triple systems. Our principal proof technique applied is the difference method. Finally, this work contains a result on packing of complete mixed graphs on v vertices, Mv, with isomorphic copies of two of the mixed triples and a possible leave structure.
"]},{"key":"dc:title","label":"Title","values":["Bicyclic Mixed Triple Systems."]}]}],"canonical_facts":{"dc:creator":["Bobga, Benkam Benedict"],"dc:date.issued":["2005-08-16T07:00:00Z"],"dc:description.abstract":["In the study of triple systems, one question faced is that of finding for what order a decomposition exists. We state and prove a necessary and sufficient condition for the existence of a bicyclic mixed triple system based on the three possible partial orientations of the 3-cycle with twice as many arcs as edges. We also explore the existence of rotational and reverse mixed triple systems. Our principal proof technique applied is the difference method. Finally, this work contains a result on packing of complete mixed graphs on v vertices, Mv, with isomorphic copies of two of the mixed triples and a possible leave structure.
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