{"id":{"repo_id":"etsu","oai_identifier":"oai:dc.etsu.edu:etd-2304"},"canonical_url":"https://search.dev.ndltd.org/etd/etsu/oai:dc.etsu.edu:etd-2304","repository":{"repo_id":"etsu","name":"East Tennessee State University","base_url":"https://dc.etsu.edu/do/oai/"},"display":{"title":"Very Cost Effective Partitions in Graphs","abstract":"<p>For a graph G=(V,E) and a set of vertices S, a vertex v in S is said to be very cost effective if it is adjacent to more vertices in V -S than in S.</p> <p>A bipartition pi={S, V- S} is called very cost effective if both S and V- S are very cost effective sets. Not all graphs have a very cost effective bipartition, for example, the complete graphs of odd order do not. We consider several families of graphs G, including Cartesian products and cacti graphs, to determine whether G has a very cost effective bipartition.</p>","abstract_html":"&lt;p&gt;For a graph G=(V,E) and a set of vertices S, a vertex v in S is said to be very cost effective if it is adjacent to more vertices in V -S than in S.&lt;/p&gt; &lt;p&gt;A bipartition pi={S, V- S} is called very cost effective if both S and V- S are very cost effective sets. Not all graphs have a very cost effective bipartition, for example, the complete graphs of odd order do not. We consider several families of graphs G, including Cartesian products and cacti graphs, to determine whether G has a very cost effective bipartition.&lt;/p&gt;","abstract_has_math":false,"creators":["Vasylieva, Inna"],"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":2013,"date_issued":"2013-05-01T07:00:00Z","date_published":"2013-05-01T07:00:00Z","updated_at":"2026-07-24T02:19:59Z","subjects":["very cost effective partition","Cartesian product","cactus graph","Discrete Mathematics and Combinatorics","Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1137","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Vasylieva, Inna"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-04-03T07:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-05-01T07:00:00Z"]},{"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":["very cost effective partition","Cartesian product","cactus graph","Discrete Mathematics and Combinatorics","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/2304/viewcontent/VasylievaI042313f.pdf","https://dc.etsu.edu/etd/1137"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>For a graph G=(V,E) and a set of vertices S, a vertex v in S is said to be very cost effective if it is adjacent to more vertices in V -S than in S.</p> <p>A bipartition pi={S, V- S} is called very cost effective if both S and V- S are very cost effective sets. Not all graphs have a very cost effective bipartition, for example, the complete graphs of odd order do not. We consider several families of graphs G, including Cartesian products and cacti graphs, to determine whether G has a very cost effective bipartition.</p>"]},{"key":"dc:title","label":"Title","values":["Very Cost Effective Partitions in Graphs"]}]}],"canonical_facts":{"dc:creator":["Vasylieva, Inna"],"dc:date.available":["2013-04-03T07:00:00Z"],"dc:date.issued":["2013-05-01T07:00:00Z"],"dc:description.abstract":["<p>For a graph G=(V,E) and a set of vertices S, a vertex v in S is said to be very cost effective if it is adjacent to more vertices in V -S than in S.</p> <p>A bipartition pi={S, V- S} is called very cost effective if both S and V- S are very cost effective sets. Not all graphs have a very cost effective bipartition, for example, the complete graphs of odd order do not. We consider several families of graphs G, including Cartesian products and cacti graphs, to determine whether G has a very cost effective bipartition.</p>"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/2304/viewcontent/VasylievaI042313f.pdf","https://dc.etsu.edu/etd/1137"],"dc:rights":["Copyright by the authors."],"dc:subject":["very cost effective partition","Cartesian product","cactus graph","Discrete Mathematics and Combinatorics","Mathematics"],"dc:title":["Very Cost Effective Partitions in Graphs"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:19:59Z"}