Constructing integer-magic graphs via the Combinatorial Nullstellensatz

Abstract

Let A be a nontrivial additive 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 construct nontrivial classes of Z p -magic graphs, prime p ≥ 3. For these graphs, some lower bounds on the number of distinct Z p -magic labelings are also established.