Group distance magic labeling of tetravalent circulant graphs

Abstract

Let G=(V,E) be a finite simple graph of order n and let Γ be an abelian group of order n. A Γ-distance magic labeling of G is a bijection φ:V⟶Γ for which there exists γ∈Γ such that ∑x∈N(v)φ(x)=γ for any v∈V, where N(v) is the neighborhood of v. In this paper, we classify all connected tetravalent circulant graphs which admit a Γ-distance magic labeling for any given finite abelian group Γ.