{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1307"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1307","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"On the minimum rank of certain graphs with path cover number 2","abstract":"The minimum rank problem is an interesting and ongoing problem in spectral graph theory which seeks to answer the question \"Given a simple graph G what is the minimum rank of a matrix whose off-diagonal zero/nonzero pattern is described by G?\" In recent years, the minimum rank of trees, unicyclic graphs, and cases of extreme minimum rank have been completely characterized. However, little is known about other families of graphs. Recent work in zero-forcing parameters, minimum semidefinite rank, and ranks of outerplanar graphs have given more ways to calculate upper and lower bounds for the minimum rank of a graph. We define a family of graphs with path cover number two and consider restrictions on the structure and minimum rank of these types of graphs. We consider a sub-family of these graphs and calculate the zero-forcing number and the positive semidefinite minimum rank. We also conjecture toward the minimum rank of these graphs.","abstract_html":"The minimum rank problem is an interesting and ongoing problem in spectral graph theory which seeks to answer the question "Given a simple graph G what is the minimum rank of a matrix whose off-diagonal zero/nonzero pattern is described by G?" In recent years, the minimum rank of trees, unicyclic graphs, and cases of extreme minimum rank have been completely characterized. However, little is known about other families of graphs. Recent work in zero-forcing parameters, minimum semidefinite rank, and ranks of outerplanar graphs have given more ways to calculate upper and lower bounds for the minimum rank of a graph. We define a family of graphs with path cover number two and consider restrictions on the structure and minimum rank of these types of graphs. We consider a sub-family of these graphs and calculate the zero-forcing number and the positive semidefinite minimum rank. We also conjecture toward the minimum rank of these graphs.","abstract_has_math":false,"creators":["Corley, Christopher M."],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Barioli, Francesco","Van der Merwe, Lucas; Smith, Ron; Ledoan, Andrew","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:46:11Z","subjects":["Graph theory (Mathematics)","Combinatorial analysis"],"languages":["English","eng"],"rights":[],"rights_urls":["https://rightsstatements.org/page/InC/1.0/?language=en"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/166","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Barioli, Francesco","Van der Merwe, Lucas; Smith, Ron; Ledoan, Andrew","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Corley, Christopher M."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-05-01T07:00:00Z"]},{"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":["Graph theory (Mathematics)","Combinatorial analysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://rightsstatements.org/page/InC/1.0/?language=en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/166"]}]},{"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 minimum rank problem is an interesting and ongoing problem in spectral graph theory which seeks to answer the question \"Given a simple graph G what is the minimum rank of a matrix whose off-diagonal zero/nonzero pattern is described by G?\" In recent years, the minimum rank of trees, unicyclic graphs, and cases of extreme minimum rank have been completely characterized. However, little is known about other families of graphs. Recent work in zero-forcing parameters, minimum semidefinite rank, and ranks of outerplanar graphs have given more ways to calculate upper and lower bounds for the minimum rank of a graph. We define a family of graphs with path cover number two and consider restrictions on the structure and minimum rank of these types of graphs. We consider a sub-family of these graphs and calculate the zero-forcing number and the positive semidefinite minimum rank. We also conjecture toward the minimum rank of these graphs."]},{"key":"dc:title","label":"Title","values":["On the minimum rank of certain graphs with path cover number 2"]}]}],"canonical_facts":{"dc:contributor":["Barioli, Francesco","Van der Merwe, Lucas; Smith, Ron; Ledoan, Andrew","College of Arts and Sciences"],"dc:creator":["Corley, Christopher M."],"dc:date":["2015-05-01T07:00:00Z"],"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 minimum rank problem is an interesting and ongoing problem in spectral graph theory which seeks to answer the question \"Given a simple graph G what is the minimum rank of a matrix whose off-diagonal zero/nonzero pattern is described by G?\" In recent years, the minimum rank of trees, unicyclic graphs, and cases of extreme minimum rank have been completely characterized. However, little is known about other families of graphs. Recent work in zero-forcing parameters, minimum semidefinite rank, and ranks of outerplanar graphs have given more ways to calculate upper and lower bounds for the minimum rank of a graph. We define a family of graphs with path cover number two and consider restrictions on the structure and minimum rank of these types of graphs. We consider a sub-family of these graphs and calculate the zero-forcing number and the positive semidefinite minimum rank. We also conjecture toward the minimum rank of these graphs."],"dc:identifier":["https://scholar.utc.edu/theses/166"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["https://rightsstatements.org/page/InC/1.0/?language=en"],"dc:subject":["Graph theory (Mathematics)","Combinatorial analysis"],"dc:title":["On the minimum rank of certain graphs with path cover number 2"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:46:11Z"}