2025/03/03 by Cichacz, Sylwia, Miklavič, Štefko
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.01423
A Γ-distance magic labeling of a graph G = (V, E) with |V| = n is a bijection ℓ from V to an Abelian group Γ of order n, for which there exists μ∈ Γ, such that the weight w(x) =∑y∈ N(x)ℓ(y) of every vertex x ∈ V is equal to μ. In this case, the element μ is called the magic constant of G. A graph G is called a group distance magic if there exists a Γ-distance magic labeling of G for every Abelian group Γ of order n. In this paper, we focused on cubic Γ-distance magic graphs as well as some properties of such graphs.