This thesis consists of research on two topics.The first topic is about different middle parts of trees, such as center, centroid, subtree core. In this work, we considered how far apart (with given order of the tree) two different `middle points' can be and when such maximum distances are achieved. We also naturally extended to trees with restricted degrees or diameter. The second topic is about trees with given degree sequence in S-order. The first trees in S-order with the additional condition that the nonleaf vertex degrees are different from each other are characterized by making use of the interpretation of the spectral moment in terms of numbers of paths and the product of adjacent vertex degrees.
","abstract_html":"<p>This thesis consists of research on two topics.The first topic is about different middle parts of trees, such as center, centroid, subtree core. In this work, we considered how far apart (with given order of the tree) two different `middle points' can be and when such maximum distances are achieved. We also naturally extended to trees with restricted degrees or diameter. The second topic is about trees with given degree sequence in S-order. The first trees in S-order with the additional condition that the nonleaf vertex degrees are different from each other are characterized by making use of the interpretation of the spectral moment in terms of numbers of paths and the product of adjacent vertex degrees.</p>","abstract_has_math":false,"creators":["Yuan, Shuai"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (restricted to Georgia Southern)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Colton Magnant","Andrew Sills"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:52Z","subjects":["ETD","Center","Centroid","Subtree Core","S-Order","Spectral Moment","Discrete Mathematics and Combinatorics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1133","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Colton Magnant","Andrew Sills"]},{"key":"dc:creator","label":"Author","values":["Yuan, Shuai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-06-18T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (restricted to Georgia Southern)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Center","Centroid","Subtree Core","S-Order","Spectral Moment","Discrete Mathematics and Combinatorics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1133"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis consists of research on two topics.The first topic is about different middle parts of trees, such as center, centroid, subtree core. In this work, we considered how far apart (with given order of the tree) two different `middle points' can be and when such maximum distances are achieved. We also naturally extended to trees with restricted degrees or diameter. The second topic is about trees with given degree sequence in S-order. The first trees in S-order with the additional condition that the nonleaf vertex degrees are different from each other are characterized by making use of the interpretation of the spectral moment in terms of numbers of paths and the product of adjacent vertex degrees.
"]},{"key":"dc:title","label":"Title","values":["Extremal Graph Theory and Enumerative Combinatorics"]}]}],"canonical_facts":{"dc:contributor":["Colton Magnant","Andrew Sills"],"dc:creator":["Yuan, Shuai"],"dc:date.available":["2014-06-18T07:00:00Z"],"dc:description.abstract":["This thesis consists of research on two topics.The first topic is about different middle parts of trees, such as center, centroid, subtree core. In this work, we considered how far apart (with given order of the tree) two different `middle points' can be and when such maximum distances are achieved. We also naturally extended to trees with restricted degrees or diameter. The second topic is about trees with given degree sequence in S-order. The first trees in S-order with the additional condition that the nonleaf vertex degrees are different from each other are characterized by making use of the interpretation of the spectral moment in terms of numbers of paths and the product of adjacent vertex degrees.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1133"],"dc:subject":["ETD","Center","Centroid","Subtree Core","S-Order","Spectral Moment","Discrete Mathematics and Combinatorics"],"dc:title":["Extremal Graph Theory and Enumerative Combinatorics"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (restricted to Georgia Southern)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:52Z"}