On closed distance magic circulants of valency up to 5

Let Γ=(V,E) be a graph of order n. A closed distance magic labeling Γ is bijection ℓ:V→{1,2,…,n} for which there exists positive integer r such that ∑x∈N[u]ℓ(x)=r all vertices u∈V, where N[u] the neighborhood u. said to if it admits labeling. In this paper, we classify connected circulants with valency at most 5, is, Cayley graphs Cay(Zn;S) |S|≤5, S=−S, 0∉S and S generates Zn.