Let G be a directed graph with a total labeling. The additive arc-weight of an arc xy is the sum of the label on xy and the label on y. The additive directed vertex-weight of a vertex x is the sum of the label on x and the labels on all arcs with head at x. The graph is additive arc magic if all additive arc-weights are equal, and is additive directed vertex magic if all vertex-weights are equal. We provide a complete characterization of all graphs which permit an additive arc magic labeling. A complete characterization of all regular graphs which may be oriented to permit an additive directed vertex magic labeling is provided. The definition of the subtractive arc-weight of an arc xy is proposed, and a correspondence between graceful labelings and subtractive arc magic labelings is shown.
Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVIV.1828/898 |
Date | 26 April 2008 |
Creators | Barone, Chedomir Angelo |
Contributors | MacGillivray, Gary |
Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
Language | English, English |
Detected Language | English |
Type | Thesis |
Rights | Available to the World Wide Web |
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