{"id":{"repo_id":"siu-theses","oai_identifier":"oai:opensiuc.lib.siu.edu:dissertations-1794"},"canonical_url":"https://search.dev.ndltd.org/etd/siu-theses/oai:opensiuc.lib.siu.edu:dissertations-1794","repository":{"repo_id":"siu-theses","name":"Southern Illinois University","base_url":"https://opensiuc.lib.siu.edu/do/oai/"},"display":{"title":"H - Removable Sequences of Graphs","abstract":"<italic>H</italic>-removable sequences, for arbitrary <italic>H</italic>, under &Lambda^* construction are presented here. In the first part we investigate Neighborhood Distinct (ND) graphs and ask some natural questions concerning disconnected <italic>H</italic> and <italic>H</italic> complement. In the second part, we introduce property * and investigate graphs that satisfy property *. Consequently we find $H$-removable sequences for all graphs <italic>H</italic> with up to 6 vertices except for G60. G60 is the only graph with up to 6 vertices for which neither it nor its complement satisfies property *. The last part of our work focuses on good and bad copies of arbitrary graphs $H$ and how to interchange from one to the other. The number of ways to count all possible copies of <italic>H</italic> in <italic>H</italic>_{pn} ^ &Lambda^* is also presented via examples.","abstract_html":"&lt;italic&gt;H&lt;/italic&gt;-removable sequences, for arbitrary &lt;italic&gt;H&lt;/italic&gt;, under &amp;Lambda^* construction are presented here. In the first part we investigate Neighborhood Distinct (ND) graphs and ask some natural questions concerning disconnected &lt;italic&gt;H&lt;/italic&gt; and &lt;italic&gt;H&lt;/italic&gt; complement. In the second part, we introduce property * and investigate graphs that satisfy property *. Consequently we find $H$-removable sequences for all graphs &lt;italic&gt;H&lt;/italic&gt; with up to 6 vertices except for G60. G60 is the only graph with up to 6 vertices for which neither it nor its complement satisfies property *. The last part of our work focuses on good and bad copies of arbitrary graphs $H$ and how to interchange from one to the other. The number of ways to count all possible copies of &lt;italic&gt;H&lt;/italic&gt; in &lt;italic&gt;H&lt;/italic&gt;_{pn} ^ &amp;Lambda^* is also presented via examples.","abstract_has_math":true,"creators":["Adatorwovor, Dayana"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Campus Only Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["McSorley, John"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-05-01T07:00:00Z","date_published":"2014-05-01T07:00:00Z","updated_at":"2026-07-24T04:34:20Z","subjects":["automorphisms","graph","neighborhood distinct","removable","removable sequences","sequences"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/791","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["McSorley, John"]},{"key":"dc:creator","label":"Author","values":["Adatorwovor, Dayana"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Only Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["automorphisms","graph","neighborhood distinct","removable","removable sequences","sequences"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/791"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<italic>H</italic>-removable sequences, for arbitrary <italic>H</italic>, under &Lambda^* construction are presented here. In the first part we investigate Neighborhood Distinct (ND) graphs and ask some natural questions concerning disconnected <italic>H</italic> and <italic>H</italic> complement. In the second part, we introduce property * and investigate graphs that satisfy property *. Consequently we find $H$-removable sequences for all graphs <italic>H</italic> with up to 6 vertices except for G60. G60 is the only graph with up to 6 vertices for which neither it nor its complement satisfies property *. The last part of our work focuses on good and bad copies of arbitrary graphs $H$ and how to interchange from one to the other. The number of ways to count all possible copies of <italic>H</italic> in <italic>H</italic>_{pn} ^ &Lambda^* is also presented via examples."]},{"key":"dc:title","label":"Title","values":["H - Removable Sequences of Graphs"]}]}],"canonical_facts":{"dc:contributor":["McSorley, John"],"dc:creator":["Adatorwovor, Dayana"],"dc:description.abstract":["<italic>H</italic>-removable sequences, for arbitrary <italic>H</italic>, under &Lambda^* construction are presented here. In the first part we investigate Neighborhood Distinct (ND) graphs and ask some natural questions concerning disconnected <italic>H</italic> and <italic>H</italic> complement. In the second part, we introduce property * and investigate graphs that satisfy property *. Consequently we find $H$-removable sequences for all graphs <italic>H</italic> with up to 6 vertices except for G60. G60 is the only graph with up to 6 vertices for which neither it nor its complement satisfies property *. The last part of our work focuses on good and bad copies of arbitrary graphs $H$ and how to interchange from one to the other. The number of ways to count all possible copies of <italic>H</italic> in <italic>H</italic>_{pn} ^ &Lambda^* is also presented via examples."],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/791"],"dc:subject":["automorphisms","graph","neighborhood distinct","removable","removable sequences","sequences"],"dc:title":["H - Removable Sequences of Graphs"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Only Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:34:20Z"}