Group-supermagic labeling of Cartesian products of two odd cycles

A Γ-supermagic labeling of a graph G = (V,E) with |E| = k is a bijection from E to an Abelian group Γ of order k such that the sum of labels of all incident edges of every vertex x ∈ V is equal to the same element μ ∈ Γ. An existence of a Γ-supermagic labeling of Cartesian product of two cycles, Cn2Cm for every n,m ≥ 3 by Z2mn was proved recently. In this paper we present a labeling method for all Abelian groups of order 2mn where m, n are odd and greater than one.