TY - JOUR
T1 - Group-supermagic labeling of Cartesian products of two even cycles
AU - Froncek, D.
AU - Paananen, P.
AU - Sorensen, L.
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2024/8
Y1 - 2024/8
N2 - A Γ-supermagic labeling of a graph G=(V,E) with |E|=q is a bijection from E to an Abelian group Γ of order q 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 Cm□Cn for every m,n≥3 by Z2mn and for any two odd cycles Cm□Cn for any m,n≥3 and any Abelian group Γ of order 2mn was proved recently. In this paper we completely solve the case of m,n both even and present a labeling method for all Abelian groups of order 2mn, where m,n are even and greater than two.
AB - A Γ-supermagic labeling of a graph G=(V,E) with |E|=q is a bijection from E to an Abelian group Γ of order q 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 Cm□Cn for every m,n≥3 by Z2mn and for any two odd cycles Cm□Cn for any m,n≥3 and any Abelian group Γ of order 2mn was proved recently. In this paper we completely solve the case of m,n both even and present a labeling method for all Abelian groups of order 2mn, where m,n are even and greater than two.
KW - Cartesian product of cycles
KW - Group supermagic labeling
KW - Magic-type labeling
KW - Supermagic labeling
KW - Vertex-magic edge labeling
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U2 - 10.1016/j.disc.2023.113741
DO - 10.1016/j.disc.2023.113741
M3 - Article
AN - SCOPUS:85174323796
SN - 0012-365X
VL - 347
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 8
M1 - 113741
ER -