{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-2179"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-2179","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"The induced path number of complementary prisms","abstract":"The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect matching between the corresponding vertices of G and G. The induced path number, denoted ρ(G), of a graph G is defined as the minimum number of subsets that the vertex set of G can be partitioned into such that each subset induces a path. In this paper, we study the induced path number of complementary prisms of complete graphs, stars, paths, and cycles.","abstract_html":"The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect matching between the corresponding vertices of G and G. The induced path number, denoted ρ(G), of a graph G is defined as the minimum number of subsets that the vertex set of G can be partitioned into such that each subset induces a path. In this paper, we study the induced path number of complementary prisms of complete graphs, stars, paths, and cycles.","abstract_has_math":false,"creators":["Downs, Michael"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Walters, Terry","Cetinkaya, Fatma Ayça; Nichols, Roger","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-05-31T07:00:00Z","date_published":"2026-05-31T07:00:00Z","updated_at":"2026-07-24T05:47:21Z","subjects":["Combinatorial analysis","Graph theory","Mathematical optimization"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/987","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Walters, Terry","Cetinkaya, Fatma Ayça; Nichols, Roger","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Downs, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-05-01T07:00:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-31T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Masters theses","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Combinatorial analysis","Graph theory","Mathematical optimization"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/987"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Mathematics","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."]},{"key":"dc:description.abstract","label":"Abstract","values":["The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect matching between the corresponding vertices of G and G. The induced path number, denoted ρ(G), of a graph G is defined as the minimum number of subsets that the vertex set of G can be partitioned into such that each subset induces a path. In this paper, we study the induced path number of complementary prisms of complete graphs, stars, paths, and cycles."]},{"key":"dc:title","label":"Title","values":["The induced path number of complementary prisms"]}]}],"canonical_facts":{"dc:contributor":["Walters, Terry","Cetinkaya, Fatma Ayça; Nichols, Roger","College of Arts and Sciences"],"dc:creator":["Downs, Michael"],"dc:date":["2025-05-01T07:00:00Z"],"dc:date.available":["2026-05-31T07:00:00Z"],"dc:description":["Dept. of Mathematics","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."],"dc:description.abstract":["The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect matching between the corresponding vertices of G and G. The induced path number, denoted ρ(G), of a graph G is defined as the minimum number of subsets that the vertex set of G can be partitioned into such that each subset induces a path. In this paper, we study the induced path number of complementary prisms of complete graphs, stars, paths, and cycles."],"dc:identifier":["https://scholar.utc.edu/theses/987"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Combinatorial analysis","Graph theory","Mathematical optimization"],"dc:title":["The induced path number of complementary prisms"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:47:21Z"}