In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of:
(1) a single cycle of length v,
(2) f fixed points and a cycle of length v − f, or
(3) two disjoint cycles.
The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of Kv.
","abstract_html":"<p>In this paper, we consider decompositions of the complete graph on <em>v</em> vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of:</p><p>(1) a single cycle of length <em>v</em>,</p><p>(2) <em>f</em> fixed points and a cycle of length <em>v</em> − <em>f</em>, or</p><p>(3) two disjoint cycles.</p><p>The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, <em>f</em>-cyclic, and bicyclic <em>Q</em>-decompositions of <em>K<sub>v</sub></em>.</p>","abstract_has_math":false,"creators":["Cantrell, Daniel Shelton"],"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":2009,"date_issued":"2009-05-09T07:00:00Z","date_published":"2009-05-09T07:00:00Z","updated_at":"2026-07-24T02:21:03Z","subjects":["coverings","packings","decompositions","graph theory","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/1872","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Cantrell, Daniel Shelton"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2009-05-09T07:00:00Z"]},{"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","decompositions","graph theory","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/3224/viewcontent/CantrellD121708f.pdf","https://dc.etsu.edu/etd/1872"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of:
(1) a single cycle of length v,
(2) f fixed points and a cycle of length v − f, or
(3) two disjoint cycles.
The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of Kv.
"]},{"key":"dc:title","label":"Title","values":["Cyclic, f-Cyclic, and Bicyclic Decompositions of the Complete Graph into the 4-Cycle with a Pendant Edge."]}]}],"canonical_facts":{"dc:creator":["Cantrell, Daniel Shelton"],"dc:date.issued":["2009-05-09T07:00:00Z"],"dc:description.abstract":["In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of:
(1) a single cycle of length v,
(2) f fixed points and a cycle of length v − f, or
(3) two disjoint cycles.
The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of Kv.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3224/viewcontent/CantrellD121708f.pdf","https://dc.etsu.edu/etd/1872"],"dc:rights":["Copyright by the authors."],"dc:subject":["coverings","packings","decompositions","graph theory","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Cyclic, f-Cyclic, and Bicyclic Decompositions of the Complete Graph into the 4-Cycle with a Pendant Edge."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:21:03Z"}