A set of vertices S in a graph G is a global dominating set (GDS) of G if S is a dominating set for both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.
","abstract_html":"<p>A set of vertices <i>S</i> in a graph <i>G</i> is a global dominating set (GDS) of <i>G</i> if <i>S</i> is a dominating set for both <i>G</i> and its complement <i>G</i>. The minimum cardinality of a global dominating set of <i>G</i> is the global domination number of <i>G</i>. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.</p>","abstract_has_math":false,"creators":["Harris, Elizabeth Marie"],"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":2012,"date_issued":"2012-08-15T07:00:00Z","date_published":"2012-08-15T07:00:00Z","updated_at":"2026-07-24T02:20:31Z","subjects":["Global Domination","Graph Theory","Stable","Mathematics","Discrete Mathematics and Combinatorics","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1476","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Harris, Elizabeth Marie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2012-08-15T07:00:00Z"]},{"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":["Global Domination","Graph Theory","Stable","Mathematics","Discrete Mathematics and Combinatorics","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/2669/viewcontent/HarrisE072712f.pdf","https://dc.etsu.edu/etd/1476"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A set of vertices S in a graph G is a global dominating set (GDS) of G if S is a dominating set for both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.
"]},{"key":"dc:title","label":"Title","values":["Global Domination Stable Graphs"]}]}],"canonical_facts":{"dc:creator":["Harris, Elizabeth Marie"],"dc:date.issued":["2012-08-15T07:00:00Z"],"dc:description.abstract":["A set of vertices S in a graph G is a global dominating set (GDS) of G if S is a dominating set for both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/2669/viewcontent/HarrisE072712f.pdf","https://dc.etsu.edu/etd/1476"],"dc:rights":["Copyright by the authors."],"dc:subject":["Global Domination","Graph Theory","Stable","Mathematics","Discrete Mathematics and Combinatorics","Physical Sciences and Mathematics"],"dc:title":["Global Domination Stable Graphs"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:20:31Z"}