In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or bipartite, and we will obtain bounds on the chromatic number of a complementary prism. We will finish the thesis with a section on possible future problems.
","abstract_html":"<p>In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the <em>distance</em> - <em>k</em> domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or bipartite, and we will obtain bounds on the chromatic number of a complementary prism. We will finish the thesis with a section on possible future problems.</p>","abstract_has_math":false,"creators":["DesOrmeaux, Wyatt Jules"],"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":"2008-12-13T08:00:00Z","date_published":"2008-12-13T08:00:00Z","updated_at":"2026-07-24T02:21:11Z","subjects":["chromatic number","complementary prism","graph theory","stratification","distance-k domination","2-step domination","restrained domination","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/1998","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["DesOrmeaux, Wyatt Jules"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2008-12-13T08:00:00Z"]},{"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":["chromatic number","complementary prism","graph theory","stratification","distance-k domination","2-step domination","restrained domination","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/3350/viewcontent/DesOrmeauxW092408f.PDF","https://dc.etsu.edu/etd/1998"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or bipartite, and we will obtain bounds on the chromatic number of a complementary prism. We will finish the thesis with a section on possible future problems.
"]},{"key":"dc:title","label":"Title","values":["Restrained and Other Domination Parameters in Complementary Prisms."]}]}],"canonical_facts":{"dc:creator":["DesOrmeaux, Wyatt Jules"],"dc:date.issued":["2008-12-13T08:00:00Z"],"dc:description.abstract":["In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or bipartite, and we will obtain bounds on the chromatic number of a complementary prism. We will finish the thesis with a section on possible future problems.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3350/viewcontent/DesOrmeauxW092408f.PDF","https://dc.etsu.edu/etd/1998"],"dc:rights":["Copyright by the authors."],"dc:subject":["chromatic number","complementary prism","graph theory","stratification","distance-k domination","2-step domination","restrained domination","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Restrained and Other Domination Parameters in 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"}