Physical Sciences and Mathematics Commons^™

Application Of The Combinatorial Nullstellensatz To Integer-Magic Graph Labelings, Richard M. Low, Dan Roberts

Theory and Applications of Graphs

Let A be a nontrivial abelian group and A* = A \ {0}. A graph is A-magic if there exists an edge labeling f using elements of A* which induces a constant vertex labeling of the graph. Such a labeling f is called an A-magic labeling and the constant value of the induced vertex labeling is called an A-magic value. In this paper, we use the Combinatorial Nullstellensatz to show the existence of Ζ_p-magic labelings (prime p ≥ 3 ) for various graphs, without having to construct the Ζ_p-magic labelings. Through many …