2022/12/23 by Fernández, Blas, Maleki, Roghayeh, Miklavič, Štefko +1 · 1 citation
#05C25 #05C50 #05C78 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2212.12441
Let Γ=(V,E) be a graph of order n. A \em closed distance magic labeling of Γ is a bijection ℓ : V → \1,2, …, n\ for which there exists a positive integer r such that ∑x ∈ N[u] ℓ(x) = r for all vertices u ∈ V, where N[u] is the closed neighborhood of u. A graph is said to be \em closed distance magic if it admits a closed distance magic labeling. In this paper, we classify all connected closed distance magic circulants with valency at most 5, that is, Cayley graphs Cay(ℤn;S) where |S| ≤ 5 and S generates ℤn.