The eccentricity of a vertex, v, of a connected graph, G, is the distance to a furthest vertex from v. A mode vertex of a connected graph, G, is a vertex whose eccentricity occurs as often in the eccentricity sequence of G as the eccentricity of any other vertex. The mode of a graph, G, is the subgraph induced by the mode vertices of G. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some results based on these definitions.
","abstract_html":"<p>The eccentricity of a vertex, <em>v</em>, of a connected graph, <em>G</em>, is the distance to a furthest vertex from <em>v</em>. A mode vertex of a connected graph, <em>G</em>, is a vertex whose eccentricity occurs as often in the eccentricity sequence of <em>G</em> as the eccentricity of any other vertex. The mode of a graph, <em>G</em>, is the subgraph induced by the mode vertices of <em>G</em>. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some results based on these definitions.</p>","abstract_has_math":false,"creators":["Kauffman, Jobriath Scott"],"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":2000,"date_issued":"2000-05-01T07:00:00Z","date_published":"2000-05-01T07:00:00Z","updated_at":"2026-07-24T02:18:50Z","subjects":["Graph theory","mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/10","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kauffman, Jobriath Scott"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2000-01-01T08:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2000-05-01T07:00:00Z"]},{"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":["Graph theory","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/1042/viewcontent/Thesis2.pdf","https://dc.etsu.edu/etd/10"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The eccentricity of a vertex, v, of a connected graph, G, is the distance to a furthest vertex from v. A mode vertex of a connected graph, G, is a vertex whose eccentricity occurs as often in the eccentricity sequence of G as the eccentricity of any other vertex. The mode of a graph, G, is the subgraph induced by the mode vertices of G. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some results based on these definitions.
"]},{"key":"dc:title","label":"Title","values":["Mode Vertices and Mode Graphs."]}]}],"canonical_facts":{"dc:creator":["Kauffman, Jobriath Scott"],"dc:date.available":["2000-01-01T08:00:00Z"],"dc:date.issued":["2000-05-01T07:00:00Z"],"dc:description.abstract":["The eccentricity of a vertex, v, of a connected graph, G, is the distance to a furthest vertex from v. A mode vertex of a connected graph, G, is a vertex whose eccentricity occurs as often in the eccentricity sequence of G as the eccentricity of any other vertex. The mode of a graph, G, is the subgraph induced by the mode vertices of G. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some results based on these definitions.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/1042/viewcontent/Thesis2.pdf","https://dc.etsu.edu/etd/10"],"dc:rights":["Copyright by the authors."],"dc:subject":["Graph theory","mathematics","Physical Sciences and Mathematics"],"dc:title":["Mode Vertices and Mode Graphs."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:18:50Z"}