Let G = (V (G), E(G)) be a graph and G̅ be the complement of G. The complementary prism of G, denoted GG̅, is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. A set D ⊆ V (G) is a locating-dominating set of G if for every u ∈ V (G)D, its neighborhood N(u)⋂D is nonempty and distinct from N(v)⋂D for all v ∈ V (G)D where v ≠ u. The locating-domination number of G is the minimum cardinality of a locating-dominating set of G. In this thesis, we study the locating-domination number of complementary prisms. We determine the locating-domination number of GG̅ for specific graphs and characterize the complementary prisms with small locating-domination numbers. We also present bounds on the locating-domination numbers of complementary prisms.
","abstract_html":"<p>Let <em>G</em> = (<em>V</em> (<em>G</em>), <em>E</em>(<em>G</em>)) be a graph and <em>G̅</em> be the complement of <em>G</em>. The complementary prism of <em>G</em>, denoted <em>GG̅</em>, is the graph formed from the disjoint union of <em>G</em> and <em>G̅</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em> and <em>G̅</em>. A set <em>D</em> ⊆ <em>V</em> (<em>G</em>) is a locating-dominating set of <em>G</em> if for every <em>u</em> ∈ <em>V</em> (<em>G</em>)<em>D</em>, its neighborhood <em>N</em>(<em>u</em>)⋂<em>D</em> is nonempty and distinct from <em>N</em>(<em>v</em>)⋂<em>D</em> for all <em>v</em> ∈ <em>V</em> (<em>G</em>)<em>D</em> where <em>v</em> ≠ <em>u</em>. The locating-domination number of <em>G</em> is the minimum cardinality of a locating-dominating set of <em>G</em>. In this thesis, we study the locating-domination number of complementary prisms. We determine the locating-domination number of <em>GG̅</em> for specific graphs </em> and characterize the complementary prisms with small locating-domination numbers. We also present bounds on the locating-domination numbers of complementary prisms.</p>","abstract_has_math":false,"creators":["Holmes, Kristin Renee Stone"],"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":["Locating-Domination","Complementary Prisims","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/1871","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Holmes, Kristin Renee Stone"]}]},{"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":["Locating-Domination","Complementary Prisims","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/3223/viewcontent/HolmesK041009f.pdf","https://dc.etsu.edu/etd/1871"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let G = (V (G), E(G)) be a graph and G̅ be the complement of G. The complementary prism of G, denoted GG̅, is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. A set D ⊆ V (G) is a locating-dominating set of G if for every u ∈ V (G)D, its neighborhood N(u)⋂D is nonempty and distinct from N(v)⋂D for all v ∈ V (G)D where v ≠ u. The locating-domination number of G is the minimum cardinality of a locating-dominating set of G. In this thesis, we study the locating-domination number of complementary prisms. We determine the locating-domination number of GG̅ for specific graphs and characterize the complementary prisms with small locating-domination numbers. We also present bounds on the locating-domination numbers of complementary prisms.
"]},{"key":"dc:title","label":"Title","values":["Locating-Domination in Complementary Prisms."]}]}],"canonical_facts":{"dc:creator":["Holmes, Kristin Renee Stone"],"dc:date.issued":["2009-05-09T07:00:00Z"],"dc:description.abstract":["Let G = (V (G), E(G)) be a graph and G̅ be the complement of G. The complementary prism of G, denoted GG̅, is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. A set D ⊆ V (G) is a locating-dominating set of G if for every u ∈ V (G)D, its neighborhood N(u)⋂D is nonempty and distinct from N(v)⋂D for all v ∈ V (G)D where v ≠ u. The locating-domination number of G is the minimum cardinality of a locating-dominating set of G. In this thesis, we study the locating-domination number of complementary prisms. We determine the locating-domination number of GG̅ for specific graphs and characterize the complementary prisms with small locating-domination numbers. We also present bounds on the locating-domination numbers of complementary prisms.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3223/viewcontent/HolmesK041009f.pdf","https://dc.etsu.edu/etd/1871"],"dc:rights":["Copyright by the authors."],"dc:subject":["Locating-Domination","Complementary Prisims","Domination","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Locating-Domination in Complementary Prisms."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:21:03Z"}