The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems in graph theory. A set S of vertices is defined to be a power dominating set of a graphs if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph is its power domination number. In this thesis, we investigate the power domination number of a block graph.
","abstract_html":"<p>The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems in graph theory. A set <em>S</em> of vertices is defined to be a power dominating set of a graphs if every vertex and every edge in the system is monitored by the set <em>S</em> (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph is its power domination number. In this thesis, we investigate the power domination number of a block graph.</p>","abstract_has_math":false,"creators":["Atkins, David Wayne"],"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":2003,"date_issued":"2003-08-11T07:00:00Z","date_published":"2003-08-11T07:00:00Z","updated_at":"2026-07-24T02:19:21Z","subjects":["Block Graph","Power Domination","PMU Placement","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/794","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Atkins, David Wayne"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2003-08-11T07:00:00Z"]},{"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":["Block Graph","Power Domination","PMU Placement","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/1951/viewcontent/AtkinsD080503f.pdf","https://dc.etsu.edu/etd/794"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems in graph theory. A set S of vertices is defined to be a power dominating set of a graphs if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph is its power domination number. In this thesis, we investigate the power domination number of a block graph.
"]},{"key":"dc:title","label":"Title","values":["Placing Monitoring Devices in Electric Power Networks Modeled by Block Graphs."]}]}],"canonical_facts":{"dc:creator":["Atkins, David Wayne"],"dc:date.issued":["2003-08-11T07:00:00Z"],"dc:description.abstract":["The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems in graph theory. A set S of vertices is defined to be a power dominating set of a graphs if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph is its power domination number. In this thesis, we investigate the power domination number of a block graph.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/1951/viewcontent/AtkinsD080503f.pdf","https://dc.etsu.edu/etd/794"],"dc:rights":["Copyright by the authors."],"dc:subject":["Block Graph","Power Domination","PMU Placement","Physical Sciences and Mathematics"],"dc:title":["Placing Monitoring Devices in Electric Power Networks Modeled by Block Graphs."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:19:21Z"}