The complementary prism of a graph G is obtained from a copy of G and its complement G̅ by adding a perfect matching between the corresponding vertices of G and G̅. For any graph G, a set D ⊆ V (G) is a double dominating set (DDS) if that set dominates every vertex of G twice. The double domination number, denoted γ×2(G), is the cardinality of a minimum double dominating set of G. We have proven results on graphs of small order, specific families and lower bounds on γ×2(GG̅).
","abstract_html":"<p>The complementary prism of a graph <em>G</em> is obtained from a copy of <em>G</em> and its complement <em>G̅</em> by adding a perfect matching between the corresponding vertices of <em>G</em> and <em>G̅</em>. For any graph <em>G</em>, a set <em>D</em> ⊆ <em>V</em> (<em>G</em>) is a <em>double dominating set</em> (DDS) if that set dominates every vertex of <em>G</em> twice. The <em>double domination number</em>, denoted γ<sub>×2</sub>(<em>G</em>), is the cardinality of a minimum double dominating set of <em>G</em>. We have proven results on graphs of small order, specific families and lower bounds on γ<sub>×2</sub>(GG̅).</p>","abstract_has_math":false,"creators":["Vaughan, Lamont D"],"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":2008,"date_issued":"2008-08-12T07:00:00Z","date_published":"2008-08-12T07:00:00Z","updated_at":"2026-07-24T02:21:11Z","subjects":["complementary prism","double domination","domination","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/1983","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Vaughan, Lamont D"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2008-08-12T07:00:00Z"]},{"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":["complementary prism","double domination","domination","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/3335/viewcontent/VaughanL072908f.pdf","https://dc.etsu.edu/etd/1983"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The complementary prism of a graph G is obtained from a copy of G and its complement G̅ by adding a perfect matching between the corresponding vertices of G and G̅. For any graph G, a set D ⊆ V (G) is a double dominating set (DDS) if that set dominates every vertex of G twice. The double domination number, denoted γ×2(G), is the cardinality of a minimum double dominating set of G. We have proven results on graphs of small order, specific families and lower bounds on γ×2(GG̅).
"]},{"key":"dc:title","label":"Title","values":["Double Domination of Complementary Prisms."]}]}],"canonical_facts":{"dc:creator":["Vaughan, Lamont D"],"dc:date.issued":["2008-08-12T07:00:00Z"],"dc:description.abstract":["The complementary prism of a graph G is obtained from a copy of G and its complement G̅ by adding a perfect matching between the corresponding vertices of G and G̅. For any graph G, a set D ⊆ V (G) is a double dominating set (DDS) if that set dominates every vertex of G twice. The double domination number, denoted γ×2(G), is the cardinality of a minimum double dominating set of G. We have proven results on graphs of small order, specific families and lower bounds on γ×2(GG̅).
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3335/viewcontent/VaughanL072908f.pdf","https://dc.etsu.edu/etd/1983"],"dc:rights":["Copyright by the authors."],"dc:subject":["complementary prism","double domination","domination","graph theory","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Double Domination of Complementary Prisms."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:21:11Z"}