Z2nm-supermagic labeling of Cn#Cm

Abstract

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. We present a Z_2nm-supermagic labeling of Cartesian product of two cycles, C_n□C_m for n odd. This along with an earlier result by Ivančo proves that a Z_2nm-supermagic labeling of C_n□C_m exists for every n, m ≥ 3.