Note on diagonal construction of Z2nm-supermagic labeling of Cn□Cm. Issue 3 (1st September 2020)

• Record Type: Journal Article
• Authors: Froncek, Dalibor; McKeown, Michael
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 17:Issue 3(2020)
• Page Start: 952
• Page End: 954
• Publication Date: 2020-09-01
• Subjects: Magic-type labeling -- supermagic labeling -- vertex-magic edge labeling -- group supermagic labeling -- Cartesian product of cycles; 05C78
• DOI: 10.1016/j.akcej.2019.08.009
• Languages: English
• ISSNs: 0972-8600

Abstract

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 . An existence of a Z 2 n m -supermagic labeling of Cartesian product of two cycles, C n □ C m for n odd was proved recently. This along with an earlier result by Ivančo proved the existence of a Z 2 n m -supermagic labeling of C n □ C m for every n, m ≥ 3 . In this paper we present a simple unified labeling method for all n, m ≥ 3 .