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Magic labelings of directed graphs

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.

  1. http://hdl.handle.net/1828/898
Identiferoai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/898
Date26 April 2008
CreatorsBarone, Chedomir Angelo
ContributorsMacGillivray, Gary
Source SetsUniversity of Victoria
LanguageEnglish, English
Detected LanguageEnglish
TypeThesis
RightsAvailable to the World Wide Web

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