{"id":{"repo_id":"etsu","oai_identifier":"oai:dc.etsu.edu:etd-3390"},"canonical_url":"https://search.dev.ndltd.org/etd/etsu/oai:dc.etsu.edu:etd-3390","repository":{"repo_id":"etsu","name":"East Tennessee State University","base_url":"https://dc.etsu.edu/do/oai/"},"display":{"title":"Decompositions, Packings, and Coverings of Complete Directed Gaphs with a 3-Circuit and a Pendent Arc.","abstract":"<p>In the study of Graph theory, there are eight orientations of the complete graph on three vertices with a pendant edge, <em>K</em><sub>3</sub> &#8746; {<em>e</em>}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings, and coverings of the complete digraph with the two 3-circuit with a pendant arc orientations.</p>","abstract_html":"&lt;p&gt;In the study of Graph theory, there are eight orientations of the complete graph on three vertices with a pendant edge, &lt;em&gt;K&lt;/em&gt;&lt;sub&gt;3&lt;/sub&gt; &amp;#8746; {&lt;em&gt;e&lt;/em&gt;}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings, and coverings of the complete digraph with the two 3-circuit with a pendant arc orientations.&lt;/p&gt;","abstract_has_math":false,"creators":["Gwellem, Chrys"],"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":2007,"date_issued":"2007-08-14T07:00:00Z","date_published":"2007-08-14T07:00:00Z","updated_at":"2026-07-24T02:21:19Z","subjects":["Coverings","Packings","Decomposition","Digraph","3-circuit","Triple Systems.","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/2029","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Gwellem, Chrys"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2007-08-14T07:00:00Z"]},{"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":["Coverings","Packings","Decomposition","Digraph","3-circuit","Triple Systems.","Discrete Mathematics and Combinatorics","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/3390/viewcontent/GwellemC080107f.pdf","https://dc.etsu.edu/etd/2029"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>In the study of Graph theory, there are eight orientations of the complete graph on three vertices with a pendant edge, <em>K</em><sub>3</sub> &#8746; {<em>e</em>}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings, and coverings of the complete digraph with the two 3-circuit with a pendant arc orientations.</p>"]},{"key":"dc:title","label":"Title","values":["Decompositions, Packings, and Coverings of Complete Directed Gaphs with a 3-Circuit and a Pendent Arc."]}]}],"canonical_facts":{"dc:creator":["Gwellem, Chrys"],"dc:date.issued":["2007-08-14T07:00:00Z"],"dc:description.abstract":["<p>In the study of Graph theory, there are eight orientations of the complete graph on three vertices with a pendant edge, <em>K</em><sub>3</sub> &#8746; {<em>e</em>}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings, and coverings of the complete digraph with the two 3-circuit with a pendant arc orientations.</p>"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3390/viewcontent/GwellemC080107f.pdf","https://dc.etsu.edu/etd/2029"],"dc:rights":["Copyright by the authors."],"dc:subject":["Coverings","Packings","Decomposition","Digraph","3-circuit","Triple Systems.","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Decompositions, Packings, and Coverings of Complete Directed Gaphs with a 3-Circuit and a Pendent Arc."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:21:19Z"}