{"id":{"repo_id":"unlv","oai_identifier":"oai:oasis.library.unlv.edu:rtds-2589"},"canonical_url":"https://search.dev.ndltd.org/etd/unlv/oai:oasis.library.unlv.edu:rtds-2589","repository":{"repo_id":"unlv","name":"University of Nevada - Las Vegas","base_url":"https://oasis.library.unlv.edu/do/oai/"},"display":{"title":"I-magic labelings of cubic trees and n-caterpillars","abstract":"Let G be a graph with q edges, then an edge labeling L: E → {1, 2,.., q} is a bijection from the set of edges E to the set of natural numbers less than or equal to q. A graph is said to be I-magic if there exists an edge labeling such that the sum of all edge labels incident to each internal vertex has the same value, and this value is called the magic index t, while the labeling is called an I-magic labeling. It has been conjectured that all cubic trees are I-magic. In this paper, we develop methods for finding I-magic labelings and determine boundary conditions for the magic index of given tRees We also classify an infinite subclass of cubic trees which are I-magic, namely cubic caterpillars. Furthermore, we classify all n-caterpillars as I-magic for n ≥ 3.","abstract_html":"Let G be a graph with q edges, then an edge labeling L: E → {1, 2,.., q} is a bijection from the set of edges E to the set of natural numbers less than or equal to q. A graph is said to be I-magic if there exists an edge labeling such that the sum of all edge labels incident to each internal vertex has the same value, and this value is called the magic index t, while the labeling is called an I-magic labeling. It has been conjectured that all cubic trees are I-magic. In this paper, we develop methods for finding I-magic labelings and determine boundary conditions for the magic index of given tRees We also classify an infinite subclass of cubic trees which are I-magic, namely cubic caterpillars. Furthermore, we classify all n-caterpillars as I-magic for n ≥ 3.","abstract_has_math":false,"creators":["Ethier, John Thomas"],"institution":"University of Nevada, Las Vegas","degree_name":"Master of Science (MS)","degree_level":"Thesis","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Michelle Schultz"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-01-01T08:00:00Z","date_published":"2003-01-01T08:00:00Z","updated_at":"2026-07-24T05:25:40Z","subjects":[],"languages":["English"],"rights":["IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://oasis.library.unlv.edu/rtds/1590"],"render_values":[{"text":"https://oasis.library.unlv.edu/rtds/1590","href":"https://oasis.library.unlv.edu/rtds/1590","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.25669/zs5c-3kpc","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Michelle Schultz"]},{"key":"dc:creator","label":"Author","values":["Ethier, John Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["University of Nevada, Las Vegas"]},{"key":"dc:type","label":"Dc Type","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.25669/zs5c-3kpc","https://oasis.library.unlv.edu/rtds/1590","https://oasis.library.unlv.edu/context/rtds/article/2589/viewcontent/uc.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let G be a graph with q edges, then an edge labeling L: E → {1, 2,.., q} is a bijection from the set of edges E to the set of natural numbers less than or equal to q. A graph is said to be I-magic if there exists an edge labeling such that the sum of all edge labels incident to each internal vertex has the same value, and this value is called the magic index t, while the labeling is called an I-magic labeling. It has been conjectured that all cubic trees are I-magic. In this paper, we develop methods for finding I-magic labelings and determine boundary conditions for the magic index of given tRees We also classify an infinite subclass of cubic trees which are I-magic, namely cubic caterpillars. Furthermore, we classify all n-caterpillars as I-magic for n ≥ 3."]},{"key":"dc:format","label":"Dc Format","values":["pdf"]},{"key":"dc:title","label":"Title","values":["I-magic labelings of cubic trees and n-caterpillars"]}]}],"canonical_facts":{"dc:contributor":["Michelle Schultz"],"dc:creator":["Ethier, John Thomas"],"dc:description.abstract":["Let G be a graph with q edges, then an edge labeling L: E → {1, 2,.., q} is a bijection from the set of edges E to the set of natural numbers less than or equal to q. A graph is said to be I-magic if there exists an edge labeling such that the sum of all edge labels incident to each internal vertex has the same value, and this value is called the magic index t, while the labeling is called an I-magic labeling. It has been conjectured that all cubic trees are I-magic. In this paper, we develop methods for finding I-magic labelings and determine boundary conditions for the magic index of given tRees We also classify an infinite subclass of cubic trees which are I-magic, namely cubic caterpillars. Furthermore, we classify all n-caterpillars as I-magic for n ≥ 3."],"dc:format":["pdf"],"dc:identifier":["10.25669/zs5c-3kpc","https://oasis.library.unlv.edu/rtds/1590","https://oasis.library.unlv.edu/context/rtds/article/2589/viewcontent/uc.pdf"],"dc:language":["English"],"dc:publisher":["University of Nevada, Las Vegas"],"dc:rights":["IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["I-magic labelings of cubic trees and n-caterpillars"],"dc:type":["Text"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:25:40Z"}