{"id":{"repo_id":"umn","oai_identifier":"oai:conservancy.umn.edu:11299/191213"},"canonical_url":"https://search.dev.ndltd.org/etd/umn/oai:conservancy.umn.edu:11299/191213","repository":{"repo_id":"umn","name":"University of Minnesota","base_url":"https://conservancy.umn.edu/server/oai/request"},"display":{"title":"New Methods for Magic Total Labelings of Graphs","abstract":"A \\textit{vertex magic total (VMT) labeling} of a graph $G=(V,E)$ is a bijection from the set of vertices and edges to the set of numbers defined by $\\lambda:V\\cup E\\rightarrow\\{1,2,\\dots,|V|+|E|\\}$ so that for every $x \\in V$ and some integer $k$, $w(x)=\\lambda(x)+\\sum_{y:xy\\in E}\\lambda(xy)=k$. An \\textit{edge magic total (EMT) labeling} is a bijection from the set of vertices and edges to the set of numbers defined by $\\lambda:V\\cup E\\rightarrow\\{1,2,\\dots,|V|+|E|\\}$ so that for every $xy \\in E$ and some integer $k$, $w(xy)=\\lambda(x)+\\lambda(y)+\\lambda(xy)=k$. Numerous results on labelings of many families of graphs have been published. In this thesis, we include methods that expand known VMT/EMT labelings into VMT/EMT labelings of some new families of graphs, such as unions of cycles, unions of paths, cycles with chords, tadpole graphs, braid graphs, triangular belts, wheels, fans, friendships, and more.","abstract_html":"A \\textit{vertex magic total (VMT) labeling} of a graph $G=(V,E)$ is a bijection from the set of vertices and edges to the set of numbers defined by $\\lambda:V\\cup E\\rightarrow\\{1,2,\\dots,|V|+|E|\\}$ so that for every $x \\in V$ and some integer $k$, <span class=\"etd-inline-math\">w(x)=\\lambda(x)+\\sum<sub>y:xy\\in E</sub>\\lambda(xy)=k</span>. An \\textit{edge magic total (EMT) labeling} is a bijection from the set of vertices and edges to the set of numbers defined by $\\lambda:V\\cup E\\rightarrow\\{1,2,\\dots,|V|+|E|\\}$ so that for every $xy \\in E$ and some integer $k$, $w(xy)=\\lambda(x)+\\lambda(y)+\\lambda(xy)=k$. Numerous results on labelings of many families of graphs have been published. In this thesis, we include methods that expand known VMT/EMT labelings into VMT/EMT labelings of some new families of graphs, such as unions of cycles, unions of paths, cycles with chords, tadpole graphs, braid graphs, triangular belts, wheels, fans, friendships, and more.","abstract_has_math":true,"creators":["Singgih, Inne"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-05","date_published":"2015-05","updated_at":"2026-07-24T05:19:48Z","subjects":["Edge Magic Total Labeling","Kotzig array","Vertex Magic Total Labeling"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11299/191213","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Singgih, Inne"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-11-27T21:26:21Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-11-27T21:26:21Z"]},{"key":"dc:date.issued","label":"Date","values":["2015-05"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Edge Magic Total Labeling","Kotzig array","Vertex Magic Total Labeling"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11299/191213"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["University of Minnesota M.S. thesis. May 2015. Major: Mathematics. Advisors: Dalibor Froncek, Sylwia Cichacz-Przenioslo. 1 computer file (PDF); ix, 117 pages."]},{"key":"dc:description.abstract","label":"Abstract","values":["A \\textit{vertex magic total (VMT) labeling} of a graph $G=(V,E)$ is a bijection from the set of vertices and edges to the set of numbers defined by $\\lambda:V\\cup E\\rightarrow\\{1,2,\\dots,|V|+|E|\\}$ so that for every $x \\in V$ and some integer $k$, $w(x)=\\lambda(x)+\\sum_{y:xy\\in E}\\lambda(xy)=k$. An \\textit{edge magic total (EMT) labeling} is a bijection from the set of vertices and edges to the set of numbers defined by $\\lambda:V\\cup E\\rightarrow\\{1,2,\\dots,|V|+|E|\\}$ so that for every $xy \\in E$ and some integer $k$, $w(xy)=\\lambda(x)+\\lambda(y)+\\lambda(xy)=k$. Numerous results on labelings of many families of graphs have been published. In this thesis, we include methods that expand known VMT/EMT labelings into VMT/EMT labelings of some new families of graphs, such as unions of cycles, unions of paths, cycles with chords, tadpole graphs, braid graphs, triangular belts, wheels, fans, friendships, and more."]},{"key":"dc:title","label":"Title","values":["New Methods for Magic Total Labelings of Graphs"]}]}],"canonical_facts":{"dc:creator":["Singgih, Inne"],"dc:date.accessioned":["2017-11-27T21:26:21Z"],"dc:date.available":["2017-11-27T21:26:21Z"],"dc:date.issued":["2015-05"],"dc:description":["University of Minnesota M.S. thesis. May 2015. Major: Mathematics. Advisors: Dalibor Froncek, Sylwia Cichacz-Przenioslo. 1 computer file (PDF); ix, 117 pages."],"dc:description.abstract":["A \\textit{vertex magic total (VMT) labeling} of a graph $G=(V,E)$ is a bijection from the set of vertices and edges to the set of numbers defined by $\\lambda:V\\cup E\\rightarrow\\{1,2,\\dots,|V|+|E|\\}$ so that for every $x \\in V$ and some integer $k$, $w(x)=\\lambda(x)+\\sum_{y:xy\\in E}\\lambda(xy)=k$. An \\textit{edge magic total (EMT) labeling} is a bijection from the set of vertices and edges to the set of numbers defined by $\\lambda:V\\cup E\\rightarrow\\{1,2,\\dots,|V|+|E|\\}$ so that for every $xy \\in E$ and some integer $k$, $w(xy)=\\lambda(x)+\\lambda(y)+\\lambda(xy)=k$. Numerous results on labelings of many families of graphs have been published. In this thesis, we include methods that expand known VMT/EMT labelings into VMT/EMT labelings of some new families of graphs, such as unions of cycles, unions of paths, cycles with chords, tadpole graphs, braid graphs, triangular belts, wheels, fans, friendships, and more."],"dc:identifier.uri":["http://hdl.handle.net/11299/191213"],"dc:language.iso":["en"],"dc:subject":["Edge Magic Total Labeling","Kotzig array","Vertex Magic Total Labeling"],"dc:title":["New Methods for Magic Total Labelings of Graphs"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:19:48Z"}