Vertex Magic Group Edge Labelings

A project submitted to the faculty of the graduate school of the University of Minnesota in partial fulfillment of the requirements for the degree of Master of Science. May 2017. Major: Mathematics and Statistics. Advisor: Dalibor Froncek. 1 computer file (PDF); vi, 46 pages, appendix A, Ill. (some col.)A vertex-magic group edge labeling of a graph G(V;E) with |E| = n is an injection from E to an abelian group ᴦ of order n such that the sum of labels of all incident edges of every vertex x ϵ V is equal to the same element µ ϵ ᴦ. We completely characterize all Cartesian products Cn□Cm that admit a vertex-magic group edge labeling by Z2nm, as well as provide labelings by a few other finite abelian groups