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

Dalibor Froncek (University of Minnesota Duluth)

Indonesian Journal of Combinatorics
Vol 7, No 1 (2023)

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 Z2mn-supermagic labeling of the Cartesian product of two cycles, Cm ℺ Cn for every m,n ≥ 3 was found by Froncek, McKeown, McKeown, and McKeown. In this paper we present a Zk-supermagic labeling of the direct and strong product by cyclic group Zk for any m,n ≥ 3.