Gamma-Supermagic Labeling The Products of Two Cycles

Abstract

A $\Gamma$-supermagic group edge labeling of a graph $G(V,E)$ with $|E|=g$ is an injection from $E$ to an Abelian group of order $g$ such that the sum of labels of all incident edges of every vertex $v \in V$ is equal to the same element $\gamma \in \Gamma$. We develop methods for labeling the products of two cycles $C_m \square C_n$ using a variety of external direct products of Abelian groups.