{"id":{"repo_id":"duquesne","oai_identifier":"oai:dsc.duq.edu:etd-1625"},"canonical_url":"https://search.dev.ndltd.org/etd/duquesne/oai:dsc.duq.edu:etd-1625","repository":{"repo_id":"duquesne","name":"Duquesne","base_url":"https://dsc.duq.edu/do/oai/"},"display":{"title":"Common Techniques in Graceful Tree Labeling with a New Computational Approach","abstract":"The graceful tree conjecture was first introduced over 50 years ago, and to this day it remains largely unresolved. Ideas for how to label arbitrary trees have been sparse, and so most work in this area focuses on demonstrating that particular classes of trees are graceful. In my research, I continue this effort and establish the gracefulness of some new tree types using previously developed techniques for constructing graceful trees. Meanwhile, little work has been done on developing computational methods for obtaining graceful labelings, as direct approaches are computationally infeasible for even moderately large trees. With this in mind, I have designed a new computational approach for constructing a graceful labeling for trees with sufficiently many leaves. This approach leverages information about the local structures present in a given tree in order to construct a suitable labeling. It has been shown to work for many small cases and thoughts on how to extend this approach for larger trees are put forth.","abstract_html":"The graceful tree conjecture was first introduced over 50 years ago, and to this day it remains largely unresolved. Ideas for how to label arbitrary trees have been sparse, and so most work in this area focuses on demonstrating that particular classes of trees are graceful. In my research, I continue this effort and establish the gracefulness of some new tree types using previously developed techniques for constructing graceful trees. Meanwhile, little work has been done on developing computational methods for obtaining graceful labelings, as direct approaches are computationally infeasible for even moderately large trees. With this in mind, I have designed a new computational approach for constructing a graceful labeling for trees with sufficiently many leaves. This approach leverages information about the local structures present in a given tree in order to construct a suitable labeling. It has been shown to work for many small cases and thoughts on how to extend this approach for larger trees are put forth.","abstract_has_math":false,"creators":["Guyer, Michael"],"institution":null,"degree_name":"MS","degree_level":"Immediate Access","degree_discipline":"Computational Mathematics","degree_department":null,"school":null,"contributors":["Karl Wimmer","Rachael Neilan","John Kern"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-01-01T08:00:00Z","date_published":"2016-01-01T08:00:00Z","updated_at":"2026-07-24T02:09:46Z","subjects":["Computational","Expansion","Graceful Labeling","Graph Theory","Tree"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dsc.duq.edu/etd/609","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Karl Wimmer","Rachael Neilan","John Kern"]},{"key":"dc:creator","label":"Author","values":["Guyer, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-08-03T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computational Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Immediate Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computational","Expansion","Graceful Labeling","Graph Theory","Tree"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dsc.duq.edu/etd/609"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The graceful tree conjecture was first introduced over 50 years ago, and to this day it remains largely unresolved. Ideas for how to label arbitrary trees have been sparse, and so most work in this area focuses on demonstrating that particular classes of trees are graceful. In my research, I continue this effort and establish the gracefulness of some new tree types using previously developed techniques for constructing graceful trees. Meanwhile, little work has been done on developing computational methods for obtaining graceful labelings, as direct approaches are computationally infeasible for even moderately large trees. With this in mind, I have designed a new computational approach for constructing a graceful labeling for trees with sufficiently many leaves. This approach leverages information about the local structures present in a given tree in order to construct a suitable labeling. It has been shown to work for many small cases and thoughts on how to extend this approach for larger trees are put forth."]},{"key":"dc:title","label":"Title","values":["Common Techniques in Graceful Tree Labeling with a New Computational Approach"]}]}],"canonical_facts":{"dc:contributor":["Karl Wimmer","Rachael Neilan","John Kern"],"dc:creator":["Guyer, Michael"],"dc:date.available":["2018-08-03T07:00:00Z"],"dc:description.abstract":["The graceful tree conjecture was first introduced over 50 years ago, and to this day it remains largely unresolved. Ideas for how to label arbitrary trees have been sparse, and so most work in this area focuses on demonstrating that particular classes of trees are graceful. In my research, I continue this effort and establish the gracefulness of some new tree types using previously developed techniques for constructing graceful trees. Meanwhile, little work has been done on developing computational methods for obtaining graceful labelings, as direct approaches are computationally infeasible for even moderately large trees. With this in mind, I have designed a new computational approach for constructing a graceful labeling for trees with sufficiently many leaves. This approach leverages information about the local structures present in a given tree in order to construct a suitable labeling. It has been shown to work for many small cases and thoughts on how to extend this approach for larger trees are put forth."],"dc:identifier":["https://dsc.duq.edu/etd/609"],"dc:language":["English"],"dc:subject":["Computational","Expansion","Graceful Labeling","Graph Theory","Tree"],"dc:title":["Common Techniques in Graceful Tree Labeling with a New Computational Approach"],"thesis:degree_discipline":["Computational Mathematics"],"thesis:degree_level":["Immediate Access"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T02:09:46Z"}