Γ-supermagic labeling of products of two cycles with cyclic groups

Abstract

A Γ-supermagic labeling of a graph G=(V,E) is a bijection from E to a group Γ of order |E| such that the sum of labels of all edges incident with any vertex x∈ V is equal to the same element μ ∈ Γ.

A Z_2mn-supermagic labeling of the Cartesian product of two cycles, C_m ℺ C_n for every m,n ≥ 3 was found by Froncek, McKeown, McKeown, and McKeown. In this paper we present a Z_k-supermagic labeling of the direct and strong product by cyclic group Z_k for any m,n ≥ 3.